| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$133.35377$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3632.864138$ |
1.36623 |
\( \frac{5473155207}{32} a^{5} - \frac{9124035747}{32} a^{4} - \frac{11577488627}{16} a^{3} + \frac{33234660007}{32} a^{2} + \frac{2493874337}{16} a - \frac{3229954287}{32} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{5}{2}\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 16 a - 3\) , \( 3 a^{5} - 2 a^{4} - 19 a^{3} + 7 a^{2} + 25 a - 5\) , \( \frac{3}{2} a^{5} + \frac{1}{2} a^{4} - 13 a^{3} - \frac{5}{2} a^{2} + 27 a - \frac{15}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+4a-\frac{5}{2}\right){x}{y}+\left(2a^{5}-a^{4}-12a^{3}+3a^{2}+16a-3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){x}^{2}+\left(3a^{5}-2a^{4}-19a^{3}+7a^{2}+25a-5\right){x}+\frac{3}{2}a^{5}+\frac{1}{2}a^{4}-13a^{3}-\frac{5}{2}a^{2}+27a-\frac{15}{2}$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$133.35377$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3632.864138$ |
1.36623 |
\( \frac{2665783}{8} a^{5} + \frac{763219}{8} a^{4} - \frac{9295335}{4} a^{3} - \frac{7826501}{8} a^{2} + \frac{6945009}{2} a + \frac{10150599}{8} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 5 a - \frac{3}{2}\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( -\frac{35}{2} a^{5} + \frac{59}{2} a^{4} + 71 a^{3} - \frac{211}{2} a^{2} - 5 a + \frac{13}{2}\) , \( -60 a^{5} + 101 a^{4} + 252 a^{3} - 368 a^{2} - 47 a + 32\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+5a-\frac{3}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a\right){x}^{2}+\left(-\frac{35}{2}a^{5}+\frac{59}{2}a^{4}+71a^{3}-\frac{211}{2}a^{2}-5a+\frac{13}{2}\right){x}-60a^{5}+101a^{4}+252a^{3}-368a^{2}-47a+32$ |
| 4.1-b1 |
4.1-b |
$2$ |
$2$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$133.35377$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.006065132$ |
$102232.9608$ |
2.79826 |
\( \frac{5473155207}{32} a^{5} - \frac{9124035747}{32} a^{4} - \frac{11577488627}{16} a^{3} + \frac{33234660007}{32} a^{2} + \frac{2493874337}{16} a - \frac{3229954287}{32} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 15 a - \frac{3}{2}\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 4 a^{3} + \frac{5}{2} a^{2} + 9 a - \frac{5}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( -\frac{25}{2} a^{5} + \frac{39}{2} a^{4} + 53 a^{3} - \frac{139}{2} a^{2} - 10 a + \frac{13}{2}\) , \( \frac{115}{2} a^{5} - \frac{193}{2} a^{4} - 243 a^{3} + \frac{703}{2} a^{2} + 54 a - \frac{69}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+15a-\frac{3}{2}\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-4a^{3}+\frac{5}{2}a^{2}+9a-\frac{5}{2}\right){x}^{2}+\left(-\frac{25}{2}a^{5}+\frac{39}{2}a^{4}+53a^{3}-\frac{139}{2}a^{2}-10a+\frac{13}{2}\right){x}+\frac{115}{2}a^{5}-\frac{193}{2}a^{4}-243a^{3}+\frac{703}{2}a^{2}+54a-\frac{69}{2}$ |
| 4.1-b2 |
4.1-b |
$2$ |
$2$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$133.35377$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.012130265$ |
$102232.9608$ |
2.79826 |
\( \frac{2665783}{8} a^{5} + \frac{763219}{8} a^{4} - \frac{9295335}{4} a^{3} - \frac{7826501}{8} a^{2} + \frac{6945009}{2} a + \frac{10150599}{8} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 2 a^{3} + \frac{3}{2} a^{2} - \frac{1}{2}\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 12 a - \frac{3}{2}\) , \( a^{5} - 6 a^{3} - a^{2} + 8 a\) , \( -\frac{77}{2} a^{5} + \frac{127}{2} a^{4} + 167 a^{3} - \frac{463}{2} a^{2} - 49 a + \frac{55}{2}\) , \( 236 a^{5} - 390 a^{4} - 1004 a^{3} + 1421 a^{2} + 237 a - 145\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-2a^{3}+\frac{3}{2}a^{2}-\frac{1}{2}\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+8a\right){y}={x}^{3}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+12a-\frac{3}{2}\right){x}^{2}+\left(-\frac{77}{2}a^{5}+\frac{127}{2}a^{4}+167a^{3}-\frac{463}{2}a^{2}-49a+\frac{55}{2}\right){x}+236a^{5}-390a^{4}-1004a^{3}+1421a^{2}+237a-145$ |
| 29.1-a1 |
29.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15798.85109$ |
2.97078 |
\( \frac{8616420}{29} a^{5} - \frac{14346831}{29} a^{4} - \frac{36486507}{29} a^{3} + \frac{52265140}{29} a^{2} + \frac{7985880}{29} a - \frac{5104951}{29} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 5 a^{3} - \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{3}{2}\) , \( 2 a^{5} - a^{4} - 14 a^{3} + 4 a^{2} + 22 a - 6\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 9 a - 3\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-5a^{3}-\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){x}^{2}+\left(2a^{5}-a^{4}-14a^{3}+4a^{2}+22a-6\right){x}+a^{5}-a^{4}-6a^{3}+3a^{2}+9a-3$ |
| 29.1-a2 |
29.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31597.70218$ |
2.97078 |
\( -\frac{6723585537}{841} a^{5} + \frac{2434092942}{841} a^{4} + \frac{46175236027}{841} a^{3} - \frac{9954602048}{841} a^{2} - \frac{70335747042}{841} a + \frac{18644956179}{841} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{1}{2} a^{2} + 12 a - \frac{1}{2}\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 2\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{3}{2} a^{2} + 5 a - \frac{1}{2}\) , \( \frac{7}{2} a^{5} + \frac{1}{2} a^{4} - 17 a^{3} - \frac{19}{2} a^{2} + 5 a + \frac{7}{2}\) , \( 2 a^{5} + a^{4} - 9 a^{3} - 10 a^{2} + a + 2\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{1}{2}a^{2}+12a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{3}{2}a^{2}+5a-\frac{1}{2}\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+2\right){x}^{2}+\left(\frac{7}{2}a^{5}+\frac{1}{2}a^{4}-17a^{3}-\frac{19}{2}a^{2}+5a+\frac{7}{2}\right){x}+2a^{5}+a^{4}-9a^{3}-10a^{2}+a+2$ |
| 29.1-a3 |
29.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15798.85109$ |
2.97078 |
\( -\frac{15145438788}{29} a^{5} + \frac{34962131817}{29} a^{4} + \frac{50648624451}{29} a^{3} - \frac{92638619211}{29} a^{2} - \frac{13103869419}{29} a + \frac{9006713419}{29} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{3}{2} a^{2} + 5 a + \frac{1}{2}\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 8 a + 3\) , \( a^{5} - 7 a^{3} + 12 a - 2\) , \( 2 a^{5} + 2 a^{4} - 5 a^{3} - 16 a^{2} - 19 a - 1\) , \( -\frac{5}{2} a^{5} - \frac{31}{2} a^{4} + 15 a^{3} + \frac{141}{2} a^{2} + 19 a - \frac{15}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{3}{2}a^{2}+5a+\frac{1}{2}\right){x}{y}+\left(a^{5}-7a^{3}+12a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-8a+3\right){x}^{2}+\left(2a^{5}+2a^{4}-5a^{3}-16a^{2}-19a-1\right){x}-\frac{5}{2}a^{5}-\frac{31}{2}a^{4}+15a^{3}+\frac{141}{2}a^{2}+19a-\frac{15}{2}$ |
| 29.1-a4 |
29.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1974.856386$ |
2.97078 |
\( -\frac{272995636183034269519}{707281} a^{5} + \frac{98420313732280867820}{707281} a^{4} + \frac{1875486988886634043927}{707281} a^{3} - \frac{403154431894086205192}{707281} a^{2} - \frac{2857606876069130576677}{707281} a + \frac{757228032390171888238}{707281} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{3}{2} a^{2} + 4 a + \frac{1}{2}\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 8 a - 4\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 4 a^{3} - \frac{5}{2} a^{2} + 7 a + \frac{3}{2}\) , \( -\frac{9}{2} a^{5} - \frac{11}{2} a^{4} + 40 a^{3} + \frac{51}{2} a^{2} - 71 a - \frac{31}{2}\) , \( -15 a^{5} - 6 a^{4} + 70 a^{3} + 30 a^{2} - 79 a - 37\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{3}{2}a^{2}+4a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-4a^{3}-\frac{5}{2}a^{2}+7a+\frac{3}{2}\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+8a-4\right){x}^{2}+\left(-\frac{9}{2}a^{5}-\frac{11}{2}a^{4}+40a^{3}+\frac{51}{2}a^{2}-71a-\frac{31}{2}\right){x}-15a^{5}-6a^{4}+70a^{3}+30a^{2}-79a-37$ |
| 29.1-b1 |
29.1-b |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.082790468$ |
$31429.09120$ |
2.93568 |
\( \frac{8616420}{29} a^{5} - \frac{14346831}{29} a^{4} - \frac{36486507}{29} a^{3} + \frac{52265140}{29} a^{2} + \frac{7985880}{29} a - \frac{5104951}{29} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 2 a^{3} + \frac{3}{2} a^{2} + \frac{1}{2}\) , \( -a^{5} + 7 a^{3} - 10 a + 2\) , \( a^{5} - 6 a^{3} - a^{2} + 7 a + 1\) , \( -\frac{5}{2} a^{5} + \frac{3}{2} a^{4} + 15 a^{3} - \frac{11}{2} a^{2} - 19 a + \frac{9}{2}\) , \( -a^{5} + 7 a^{3} - 11 a + 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-2a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+7a+1\right){y}={x}^{3}+\left(-a^{5}+7a^{3}-10a+2\right){x}^{2}+\left(-\frac{5}{2}a^{5}+\frac{3}{2}a^{4}+15a^{3}-\frac{11}{2}a^{2}-19a+\frac{9}{2}\right){x}-a^{5}+7a^{3}-11a+1$ |
| 29.1-b2 |
29.1-b |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.165580936$ |
$31429.09120$ |
2.93568 |
\( -\frac{6723585537}{841} a^{5} + \frac{2434092942}{841} a^{4} + \frac{46175236027}{841} a^{3} - \frac{9954602048}{841} a^{2} - \frac{70335747042}{841} a + \frac{18644956179}{841} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 15 a - 2\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 2 a^{3} + \frac{3}{2} a^{2} - \frac{1}{2}\) , \( \frac{3}{2} a^{5} - \frac{3}{2} a^{4} - 8 a^{3} + \frac{11}{2} a^{2} + 8 a - \frac{5}{2}\) , \( 5 a^{4} + 6 a^{3} - 28 a^{2} - 34 a + 11\) , \( -\frac{3}{2} a^{5} + \frac{13}{2} a^{4} + 16 a^{3} - \frac{69}{2} a^{2} - 50 a + \frac{31}{2}\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+3a^{2}+15a-2\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{3}{2}a^{4}-8a^{3}+\frac{11}{2}a^{2}+8a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-2a^{3}+\frac{3}{2}a^{2}-\frac{1}{2}\right){x}^{2}+\left(5a^{4}+6a^{3}-28a^{2}-34a+11\right){x}-\frac{3}{2}a^{5}+\frac{13}{2}a^{4}+16a^{3}-\frac{69}{2}a^{2}-50a+\frac{31}{2}$ |
| 29.1-b3 |
29.1-b |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.331161873$ |
$7857.272800$ |
2.93568 |
\( -\frac{15145438788}{29} a^{5} + \frac{34962131817}{29} a^{4} + \frac{50648624451}{29} a^{3} - \frac{92638619211}{29} a^{2} - \frac{13103869419}{29} a + \frac{9006713419}{29} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{3}{2}\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 8 a^{2} + 3\) , \( a + 1\) , \( \frac{9}{2} a^{5} - \frac{7}{2} a^{4} - 23 a^{3} + \frac{19}{2} a^{2} + 16 a - \frac{5}{2}\) , \( \frac{5}{2} a^{5} - \frac{1}{2} a^{4} - 21 a^{3} + \frac{7}{2} a^{2} + 43 a - \frac{23}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+4a-\frac{3}{2}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-8a^{2}+3\right){x}^{2}+\left(\frac{9}{2}a^{5}-\frac{7}{2}a^{4}-23a^{3}+\frac{19}{2}a^{2}+16a-\frac{5}{2}\right){x}+\frac{5}{2}a^{5}-\frac{1}{2}a^{4}-21a^{3}+\frac{7}{2}a^{2}+43a-\frac{23}{2}$ |
| 29.1-b4 |
29.1-b |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$157.28964$ |
$(1/2a^5+1/2a^4-4a^3-5/2a^2+6a-1/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.331161873$ |
$1964.318200$ |
2.93568 |
\( -\frac{272995636183034269519}{707281} a^{5} + \frac{98420313732280867820}{707281} a^{4} + \frac{1875486988886634043927}{707281} a^{3} - \frac{403154431894086205192}{707281} a^{2} - \frac{2857606876069130576677}{707281} a + \frac{757228032390171888238}{707281} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a^{5} - 6 a^{3} - a^{2} + 8 a + 1\) , \( a^{5} - 8 a^{4} + 4 a^{3} + 30 a^{2} - 30 a\) , \( 59 a^{5} + 133 a^{4} - 92 a^{3} - 277 a^{2} - 40 a + 31\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){x}{y}+\left(a^{5}-6a^{3}-a^{2}+8a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+7a+2\right){x}^{2}+\left(a^{5}-8a^{4}+4a^{3}+30a^{2}-30a\right){x}+59a^{5}+133a^{4}-92a^{3}-277a^{2}-40a+31$ |
| 36.1-a1 |
36.1-a |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{4} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1024$ |
\( 2 \) |
$1$ |
$6.942163617$ |
2.67344 |
\( \frac{24440219738032611356663}{36} a^{5} - \frac{40561631579796278917201}{36} a^{4} - \frac{51882193713025061416439}{18} a^{3} + \frac{147769887187775885902283}{36} a^{2} + \frac{5899906308447709939721}{9} a - \frac{1636259899263628386437}{4} \) |
\( \bigl[\frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 4 a^{3} - \frac{5}{2} a^{2} + 8 a + \frac{1}{2}\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{1}{2} a^{2} + 10 a + \frac{1}{2}\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 4 a^{3} - \frac{5}{2} a^{2} + 8 a + \frac{1}{2}\) , \( -\frac{509}{2} a^{5} + \frac{797}{2} a^{4} + 1132 a^{3} - \frac{2949}{2} a^{2} - 336 a + \frac{215}{2}\) , \( -\frac{11251}{2} a^{5} + \frac{18321}{2} a^{4} + 24231 a^{3} - \frac{67201}{2} a^{2} - 6024 a + \frac{6275}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-4a^{3}-\frac{5}{2}a^{2}+8a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-4a^{3}-\frac{5}{2}a^{2}+8a+\frac{1}{2}\right){y}={x}^{3}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{1}{2}a^{2}+10a+\frac{1}{2}\right){x}^{2}+\left(-\frac{509}{2}a^{5}+\frac{797}{2}a^{4}+1132a^{3}-\frac{2949}{2}a^{2}-336a+\frac{215}{2}\right){x}-\frac{11251}{2}a^{5}+\frac{18321}{2}a^{4}+24231a^{3}-\frac{67201}{2}a^{2}-6024a+\frac{6275}{2}$ |
| 36.1-a2 |
36.1-a |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$444.2984715$ |
2.67344 |
\( \frac{5693750903351}{648} a^{5} - \frac{9498846034267}{648} a^{4} - \frac{12036250271987}{324} a^{3} + \frac{34596651005327}{648} a^{2} + \frac{2565218763157}{324} a - \frac{1112749733645}{216} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{3}{2} a^{4} - 8 a^{3} + \frac{11}{2} a^{2} + 9 a - \frac{5}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 3 a - 2\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 9 a - 2\) , \( 16 a^{5} - 17 a^{4} - 74 a^{3} + 45 a^{2} + 54 a - 16\) , \( 51 a^{5} - 75 a^{4} - 204 a^{3} + 194 a^{2} + 128 a - 44\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{3}{2}a^{4}-8a^{3}+\frac{11}{2}a^{2}+9a-\frac{5}{2}\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+9a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+3a-2\right){x}^{2}+\left(16a^{5}-17a^{4}-74a^{3}+45a^{2}+54a-16\right){x}+51a^{5}-75a^{4}-204a^{3}+194a^{2}+128a-44$ |
| 36.1-a3 |
36.1-a |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$28435.10217$ |
2.67344 |
\( \frac{8437199}{288} a^{5} - \frac{14689753}{288} a^{4} - \frac{16877303}{144} a^{3} + \frac{53375555}{288} a^{2} + \frac{115795}{36} a - \frac{234077}{32} \) |
\( \bigl[a^{5} - 7 a^{3} - a^{2} + 12 a\) , \( a^{4} - 5 a^{2} + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 8 a - 3\) , \( 2 a^{5} + 2 a^{4} - 11 a^{3} - 13 a^{2} + 8 a + 8\) , \( -a^{5} + 5 a^{3} + a^{2} + 4\bigr] \) |
${y}^2+\left(a^{5}-7a^{3}-a^{2}+12a\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+8a-3\right){y}={x}^{3}+\left(a^{4}-5a^{2}+3\right){x}^{2}+\left(2a^{5}+2a^{4}-11a^{3}-13a^{2}+8a+8\right){x}-a^{5}+5a^{3}+a^{2}+4$ |
| 36.1-a4 |
36.1-a |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{2} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$28435.10217$ |
2.67344 |
\( \frac{45235}{24} a^{5} + \frac{22897}{24} a^{4} - \frac{162367}{12} a^{3} - \frac{197141}{24} a^{2} + \frac{249797}{12} a + \frac{93839}{8} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 8 a - 3\) , \( -a^{3} + 5 a\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 9 a - 2\) , \( \frac{1}{2} a^{5} - \frac{3}{2} a^{4} - 4 a^{3} + \frac{15}{2} a^{2} + 10 a - \frac{7}{2}\) , \( -a^{4} - a^{3} + 5 a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+8a-3\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+9a-2\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(\frac{1}{2}a^{5}-\frac{3}{2}a^{4}-4a^{3}+\frac{15}{2}a^{2}+10a-\frac{7}{2}\right){x}-a^{4}-a^{3}+5a^{2}+6a-2$ |
| 36.1-a5 |
36.1-a |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$28435.10217$ |
2.67344 |
\( \frac{4622393129}{1536} a^{5} + \frac{10690983971}{1536} a^{4} - \frac{3848185181}{768} a^{3} - \frac{22500976087}{1536} a^{2} - \frac{568662233}{768} a + \frac{667157733}{512} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{3}{2} a^{2} + 4 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{5} - \frac{1}{2} a^{4} + 4 a^{3} + \frac{3}{2} a^{2} - 8 a + \frac{3}{2}\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{1}{2} a^{2} + 11 a + \frac{1}{2}\) , \( -\frac{7}{2} a^{5} + \frac{11}{2} a^{4} + 19 a^{3} - \frac{43}{2} a^{2} - 16 a + \frac{9}{2}\) , \( -\frac{11}{2} a^{5} + \frac{13}{2} a^{4} + 25 a^{3} - \frac{43}{2} a^{2} - 12 a + \frac{3}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{3}{2}a^{2}+4a-\frac{1}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{1}{2}a^{2}+11a+\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}+4a^{3}+\frac{3}{2}a^{2}-8a+\frac{3}{2}\right){x}^{2}+\left(-\frac{7}{2}a^{5}+\frac{11}{2}a^{4}+19a^{3}-\frac{43}{2}a^{2}-16a+\frac{9}{2}\right){x}-\frac{11}{2}a^{5}+\frac{13}{2}a^{4}+25a^{3}-\frac{43}{2}a^{2}-12a+\frac{3}{2}$ |
| 36.1-a6 |
36.1-a |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{16} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2^{3} \) |
$1$ |
$6.942163617$ |
2.67344 |
\( -\frac{603047647289160488543}{26244} a^{5} + \frac{217832584605090651817}{26244} a^{4} + \frac{2071456737632544801887}{13122} a^{3} - \frac{893478270325584616211}{26244} a^{2} - \frac{1578152932194273431969}{6561} a + \frac{62114571328492400639}{972} \) |
\( \bigl[a^{5} - 7 a^{3} - a^{2} + 12 a\) , \( a^{4} - 5 a^{2} + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 8 a - 3\) , \( 7 a^{5} + 17 a^{4} - 51 a^{3} - 83 a^{2} + 58 a - 12\) , \( 126 a^{5} + 181 a^{4} - 708 a^{3} - 999 a^{2} + 270 a - 21\bigr] \) |
${y}^2+\left(a^{5}-7a^{3}-a^{2}+12a\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+8a-3\right){y}={x}^{3}+\left(a^{4}-5a^{2}+3\right){x}^{2}+\left(7a^{5}+17a^{4}-51a^{3}-83a^{2}+58a-12\right){x}+126a^{5}+181a^{4}-708a^{3}-999a^{2}+270a-21$ |
| 36.1-b1 |
36.1-b |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{10} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \cdot 5 \) |
$0.375950073$ |
$1050.920799$ |
4.45756 |
\( \frac{119363596101130715508791}{31104} a^{5} - \frac{1584791711401383212204293}{248832} a^{4} - \frac{1013549842519838382045241}{62208} a^{3} + \frac{2886773575864980923427715}{124416} a^{2} + \frac{922065731071830180199745}{248832} a - \frac{575375773423366437534965}{248832} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{3}{2} a^{4} - 8 a^{3} + \frac{11}{2} a^{2} + 9 a - \frac{7}{2}\) , \( a^{4} - 5 a^{2} - 2 a + 4\) , \( a^{5} - 7 a^{3} + 11 a - 2\) , \( -\frac{127}{2} a^{5} - \frac{255}{2} a^{4} + 137 a^{3} + \frac{561}{2} a^{2} - 29 a - \frac{59}{2}\) , \( 1563 a^{5} + 3564 a^{4} - 2794 a^{3} - 7789 a^{2} - 374 a + 703\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{3}{2}a^{4}-8a^{3}+\frac{11}{2}a^{2}+9a-\frac{7}{2}\right){x}{y}+\left(a^{5}-7a^{3}+11a-2\right){y}={x}^{3}+\left(a^{4}-5a^{2}-2a+4\right){x}^{2}+\left(-\frac{127}{2}a^{5}-\frac{255}{2}a^{4}+137a^{3}+\frac{561}{2}a^{2}-29a-\frac{59}{2}\right){x}+1563a^{5}+3564a^{4}-2794a^{3}-7789a^{2}-374a+703$ |
| 36.1-b2 |
36.1-b |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{4} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{3} \) |
$0.037595007$ |
$13136.50999$ |
4.45756 |
\( -\frac{1722160537}{144} a^{5} - \frac{99876907}{6} a^{4} + \frac{1453025065}{24} a^{3} + \frac{4618842167}{48} a^{2} + \frac{115469977}{48} a - \frac{309138401}{36} \) |
\( \bigl[a^{5} - 7 a^{3} - a^{2} + 11 a + 1\) , \( -a^{5} + 7 a^{3} - 10 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a\) , \( -a^{2} - 2 a + 1\) , \( 6 a^{5} - 2 a^{4} - 43 a^{3} + 8 a^{2} + 69 a - 18\bigr] \) |
${y}^2+\left(a^{5}-7a^{3}-a^{2}+11a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a\right){y}={x}^{3}+\left(-a^{5}+7a^{3}-10a+2\right){x}^{2}+\left(-a^{2}-2a+1\right){x}+6a^{5}-2a^{4}-43a^{3}+8a^{2}+69a-18$ |
| 36.1-b3 |
36.1-b |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$0.075190014$ |
$26273.01998$ |
4.45756 |
\( \frac{1102067}{3} a^{5} + \frac{1171711}{12} a^{4} - \frac{7625360}{3} a^{3} - \frac{6269761}{6} a^{2} + \frac{44939593}{12} a + \frac{16412615}{12} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 2\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 3\) , \( -\frac{7}{2} a^{5} + \frac{11}{2} a^{4} + 14 a^{3} - \frac{39}{2} a^{2} + \frac{3}{2}\) , \( \frac{3}{2} a^{5} - \frac{5}{2} a^{4} - 7 a^{3} + \frac{19}{2} a^{2} + 4 a - \frac{5}{2}\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+4a-3\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-6a-1\right){x}^{2}+\left(-\frac{7}{2}a^{5}+\frac{11}{2}a^{4}+14a^{3}-\frac{39}{2}a^{2}+\frac{3}{2}\right){x}+\frac{3}{2}a^{5}-\frac{5}{2}a^{4}-7a^{3}+\frac{19}{2}a^{2}+4a-\frac{5}{2}$ |
| 36.1-b4 |
36.1-b |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{40} \cdot 3^{20} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.187975036$ |
$525.4603997$ |
4.45756 |
\( -\frac{103658018295749822521}{61917364224} a^{5} + \frac{3794082804542854921}{2579890176} a^{4} + \frac{11193114343188612025}{1146617856} a^{3} - \frac{37967162798078400611}{6879707136} a^{2} - \frac{231502246620283083943}{20639121408} a + \frac{49584401379856072927}{15479341056} \) |
\( \bigl[\frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 4 a^{3} - \frac{5}{2} a^{2} + 8 a + \frac{3}{2}\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 5 a - \frac{3}{2}\) , \( 238 a^{5} - 394 a^{4} - 812 a^{3} + 973 a^{2} + 189 a - 103\) , \( 4807 a^{5} - 8733 a^{4} - 15773 a^{3} + 22773 a^{2} + 3499 a - 2224\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-4a^{3}-\frac{5}{2}a^{2}+8a+\frac{3}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+5a-\frac{3}{2}\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(238a^{5}-394a^{4}-812a^{3}+973a^{2}+189a-103\right){x}+4807a^{5}-8733a^{4}-15773a^{3}+22773a^{2}+3499a-2224$ |
| 36.1-c1 |
36.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{4} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$0.150591678$ |
$587.7807924$ |
3.19567 |
\( \frac{24440219738032611356663}{36} a^{5} - \frac{40561631579796278917201}{36} a^{4} - \frac{51882193713025061416439}{18} a^{3} + \frac{147769887187775885902283}{36} a^{2} + \frac{5899906308447709939721}{9} a - \frac{1636259899263628386437}{4} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 2 a^{3} + \frac{3}{2} a^{2} + \frac{1}{2}\) , \( -a^{5} + 6 a^{3} + 2 a^{2} - 6 a - 2\) , \( a^{5} - 7 a^{3} + 11 a - 2\) , \( -3685 a^{5} + 6122 a^{4} + 15663 a^{3} - 22286 a^{2} - 3589 a + 2210\) , \( \frac{502583}{2} a^{5} - \frac{833779}{2} a^{4} - 1066837 a^{3} + \frac{3037731}{2} a^{2} + 242726 a - \frac{302659}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-2a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}\right){x}{y}+\left(a^{5}-7a^{3}+11a-2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+2a^{2}-6a-2\right){x}^{2}+\left(-3685a^{5}+6122a^{4}+15663a^{3}-22286a^{2}-3589a+2210\right){x}+\frac{502583}{2}a^{5}-\frac{833779}{2}a^{4}-1066837a^{3}+\frac{3037731}{2}a^{2}+242726a-\frac{302659}{2}$ |
| 36.1-c2 |
36.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.075295839$ |
$18808.98535$ |
3.19567 |
\( \frac{5693750903351}{648} a^{5} - \frac{9498846034267}{648} a^{4} - \frac{12036250271987}{324} a^{3} + \frac{34596651005327}{648} a^{2} + \frac{2565218763157}{324} a - \frac{1112749733645}{216} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 16 a - 3\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 6 a + 2\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 4 a^{3} - \frac{5}{2} a^{2} + 7 a + \frac{3}{2}\) , \( -\frac{43}{2} a^{5} + \frac{61}{2} a^{4} + 110 a^{3} - \frac{245}{2} a^{2} - 107 a + \frac{75}{2}\) , \( \frac{173}{2} a^{5} - \frac{269}{2} a^{4} - 336 a^{3} + \frac{945}{2} a^{2} - 45 a - \frac{31}{2}\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+3a^{2}+16a-3\right){x}{y}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-4a^{3}-\frac{5}{2}a^{2}+7a+\frac{3}{2}\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+6a+2\right){x}^{2}+\left(-\frac{43}{2}a^{5}+\frac{61}{2}a^{4}+110a^{3}-\frac{245}{2}a^{2}-107a+\frac{75}{2}\right){x}+\frac{173}{2}a^{5}-\frac{269}{2}a^{4}-336a^{3}+\frac{945}{2}a^{2}-45a-\frac{31}{2}$ |
| 36.1-c3 |
36.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.037647919$ |
$75235.94143$ |
3.19567 |
\( \frac{8437199}{288} a^{5} - \frac{14689753}{288} a^{4} - \frac{16877303}{144} a^{3} + \frac{53375555}{288} a^{2} + \frac{115795}{36} a - \frac{234077}{32} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 16 a - \frac{5}{2}\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 3 a^{3} - \frac{7}{2} a^{2} + 3 a + \frac{7}{2}\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{3}{2}\) , \( -10 a^{5} + 3 a^{4} + 76 a^{3} - 20 a^{2} - 129 a + 42\) , \( -24 a^{5} + 3 a^{4} + 177 a^{3} - 22 a^{2} - 281 a + 77\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+16a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+4a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-3a^{3}-\frac{7}{2}a^{2}+3a+\frac{7}{2}\right){x}^{2}+\left(-10a^{5}+3a^{4}+76a^{3}-20a^{2}-129a+42\right){x}-24a^{5}+3a^{4}+177a^{3}-22a^{2}-281a+77$ |
| 36.1-c4 |
36.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{2} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.075295839$ |
$18808.98535$ |
3.19567 |
\( \frac{45235}{24} a^{5} + \frac{22897}{24} a^{4} - \frac{162367}{12} a^{3} - \frac{197141}{24} a^{2} + \frac{249797}{12} a + \frac{93839}{8} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{1}{2} a^{2} + 12 a + \frac{1}{2}\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 16 a - \frac{3}{2}\) , \( \frac{5}{2} a^{5} - \frac{1}{2} a^{4} - 18 a^{3} - \frac{1}{2} a^{2} + 30 a + \frac{13}{2}\) , \( \frac{7}{2} a^{5} + \frac{1}{2} a^{4} - 25 a^{3} - \frac{13}{2} a^{2} + 37 a + \frac{9}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{1}{2}a^{2}+12a+\frac{1}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+16a-\frac{3}{2}\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}^{2}+\left(\frac{5}{2}a^{5}-\frac{1}{2}a^{4}-18a^{3}-\frac{1}{2}a^{2}+30a+\frac{13}{2}\right){x}+\frac{7}{2}a^{5}+\frac{1}{2}a^{4}-25a^{3}-\frac{13}{2}a^{2}+37a+\frac{9}{2}$ |
| 36.1-c5 |
36.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.075295839$ |
$18808.98535$ |
3.19567 |
\( \frac{4622393129}{1536} a^{5} + \frac{10690983971}{1536} a^{4} - \frac{3848185181}{768} a^{3} - \frac{22500976087}{1536} a^{2} - \frac{568662233}{768} a + \frac{667157733}{512} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 8 a + 4\) , \( \frac{3}{2} a^{5} - \frac{3}{2} a^{4} - 8 a^{3} + \frac{11}{2} a^{2} + 9 a - \frac{5}{2}\) , \( -8 a^{5} + 11 a^{4} + 37 a^{3} - 43 a^{2} - 17 a + 18\) , \( \frac{11}{2} a^{5} - \frac{35}{2} a^{4} - 7 a^{3} + \frac{121}{2} a^{2} - 54 a + \frac{35}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{3}{2}a^{4}-8a^{3}+\frac{11}{2}a^{2}+9a-\frac{5}{2}\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+8a+4\right){x}^{2}+\left(-8a^{5}+11a^{4}+37a^{3}-43a^{2}-17a+18\right){x}+\frac{11}{2}a^{5}-\frac{35}{2}a^{4}-7a^{3}+\frac{121}{2}a^{2}-54a+\frac{35}{2}$ |
| 36.1-c6 |
36.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{16} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.150591678$ |
$2351.123169$ |
3.19567 |
\( -\frac{603047647289160488543}{26244} a^{5} + \frac{217832584605090651817}{26244} a^{4} + \frac{2071456737632544801887}{13122} a^{3} - \frac{893478270325584616211}{26244} a^{2} - \frac{1578152932194273431969}{6561} a + \frac{62114571328492400639}{972} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 16 a - \frac{5}{2}\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 3 a^{3} - \frac{7}{2} a^{2} + 3 a + \frac{7}{2}\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{3}{2}\) , \( 20 a^{5} - 37 a^{4} - 49 a^{3} + 90 a^{2} - 49 a - 23\) , \( 304 a^{5} - 380 a^{4} - 1107 a^{3} + 757 a^{2} + 227 a - 57\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+16a-\frac{5}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+4a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-3a^{3}-\frac{7}{2}a^{2}+3a+\frac{7}{2}\right){x}^{2}+\left(20a^{5}-37a^{4}-49a^{3}+90a^{2}-49a-23\right){x}+304a^{5}-380a^{4}-1107a^{3}+757a^{2}+227a-57$ |
| 36.1-d1 |
36.1-d |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{10} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$625$ |
\( 2 \) |
$1$ |
$6.518111700$ |
1.53206 |
\( \frac{119363596101130715508791}{31104} a^{5} - \frac{1584791711401383212204293}{248832} a^{4} - \frac{1013549842519838382045241}{62208} a^{3} + \frac{2886773575864980923427715}{124416} a^{2} + \frac{922065731071830180199745}{248832} a - \frac{575375773423366437534965}{248832} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{3}{2} a^{4} - 8 a^{3} + \frac{11}{2} a^{2} + 8 a - \frac{5}{2}\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 4 a^{3} - \frac{3}{2} a^{2} + 6 a - \frac{1}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a\) , \( -71 a^{5} - 33 a^{4} + 479 a^{3} + 259 a^{2} - 668 a - 259\) , \( -\frac{241}{2} a^{5} + \frac{845}{2} a^{4} + 1593 a^{3} - \frac{3637}{2} a^{2} - 5609 a - \frac{3457}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{3}{2}a^{4}-8a^{3}+\frac{11}{2}a^{2}+8a-\frac{5}{2}\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-4a^{3}-\frac{3}{2}a^{2}+6a-\frac{1}{2}\right){x}^{2}+\left(-71a^{5}-33a^{4}+479a^{3}+259a^{2}-668a-259\right){x}-\frac{241}{2}a^{5}+\frac{845}{2}a^{4}+1593a^{3}-\frac{3637}{2}a^{2}-5609a-\frac{3457}{2}$ |
| 36.1-d2 |
36.1-d |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{4} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$50922.74765$ |
1.53206 |
\( -\frac{1722160537}{144} a^{5} - \frac{99876907}{6} a^{4} + \frac{1453025065}{24} a^{3} + \frac{4618842167}{48} a^{2} + \frac{115469977}{48} a - \frac{309138401}{36} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a - 1\) , \( -\frac{3}{2} a^{5} + \frac{3}{2} a^{4} + 8 a^{3} - \frac{11}{2} a^{2} - 9 a + \frac{9}{2}\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 16 a - 2\) , \( -\frac{5}{2} a^{5} + \frac{9}{2} a^{4} + 15 a^{3} - \frac{33}{2} a^{2} - 26 a + \frac{5}{2}\) , \( -\frac{3}{2} a^{5} - \frac{1}{2} a^{4} + 3 a^{3} + \frac{13}{2} a^{2} + 13 a + \frac{3}{2}\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a-1\right){x}{y}+\left(2a^{5}-a^{4}-12a^{3}+3a^{2}+16a-2\right){y}={x}^{3}+\left(-\frac{3}{2}a^{5}+\frac{3}{2}a^{4}+8a^{3}-\frac{11}{2}a^{2}-9a+\frac{9}{2}\right){x}^{2}+\left(-\frac{5}{2}a^{5}+\frac{9}{2}a^{4}+15a^{3}-\frac{33}{2}a^{2}-26a+\frac{5}{2}\right){x}-\frac{3}{2}a^{5}-\frac{1}{2}a^{4}+3a^{3}+\frac{13}{2}a^{2}+13a+\frac{3}{2}$ |
| 36.1-d3 |
36.1-d |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$101845.4953$ |
1.53206 |
\( \frac{1102067}{3} a^{5} + \frac{1171711}{12} a^{4} - \frac{7625360}{3} a^{3} - \frac{6269761}{6} a^{2} + \frac{44939593}{12} a + \frac{16412615}{12} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 15 a - \frac{3}{2}\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 16 a - \frac{7}{2}\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{3}{2} a^{2} + 4 a + \frac{1}{2}\) , \( -\frac{1}{2} a^{5} + \frac{1}{2} a^{4} + 3 a^{3} - \frac{1}{2} a^{2} - 4 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{5} + \frac{1}{2} a^{4} + 3 a^{3} - \frac{3}{2} a^{2} - 4 a + \frac{1}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+15a-\frac{3}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{3}{2}a^{2}+4a+\frac{1}{2}\right){y}={x}^{3}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+16a-\frac{7}{2}\right){x}^{2}+\left(-\frac{1}{2}a^{5}+\frac{1}{2}a^{4}+3a^{3}-\frac{1}{2}a^{2}-4a-\frac{3}{2}\right){x}-\frac{1}{2}a^{5}+\frac{1}{2}a^{4}+3a^{3}-\frac{3}{2}a^{2}-4a+\frac{1}{2}$ |
| 36.1-d4 |
36.1-d |
$4$ |
$10$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{40} \cdot 3^{20} \) |
$160.14947$ |
$(a+1), (1/2a^5-1/2a^4-2a^3+3/2a^2-3/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$625$ |
\( 2^{2} \) |
$1$ |
$3.259055850$ |
1.53206 |
\( -\frac{103658018295749822521}{61917364224} a^{5} + \frac{3794082804542854921}{2579890176} a^{4} + \frac{11193114343188612025}{1146617856} a^{3} - \frac{37967162798078400611}{6879707136} a^{2} - \frac{231502246620283083943}{20639121408} a + \frac{49584401379856072927}{15479341056} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 8 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 8 a + 4\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 4 a^{3} - \frac{5}{2} a^{2} + 8 a + \frac{3}{2}\) , \( 17 a^{5} + 48 a^{4} - 101 a^{3} - 307 a^{2} - 26 a + 30\) , \( 210 a^{5} + 326 a^{4} - 1251 a^{3} - 2389 a^{2} - 56 a + 206\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+8a+1\right){x}{y}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-4a^{3}-\frac{5}{2}a^{2}+8a+\frac{3}{2}\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-8a+4\right){x}^{2}+\left(17a^{5}+48a^{4}-101a^{3}-307a^{2}-26a+30\right){x}+210a^{5}+326a^{4}-1251a^{3}-2389a^{2}-56a+206$ |
| 41.1-a1 |
41.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{12} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$16$ |
\( 2 \) |
$1$ |
$556.2235592$ |
3.34691 |
\( -\frac{4198436361667110996600488530}{22563490300366186081} a^{5} - \frac{5844757786544332783449381171}{22563490300366186081} a^{4} + \frac{21252423766059100218293843129}{22563490300366186081} a^{3} + \frac{33784506632375941559480720450}{22563490300366186081} a^{2} + \frac{849487561148946913710553326}{22563490300366186081} a - \frac{3015806472984505420487097371}{22563490300366186081} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{3}{2} a^{4} - 8 a^{3} + \frac{11}{2} a^{2} + 9 a - \frac{5}{2}\) , \( -a^{5} + 8 a^{3} - 16 a + 3\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( \frac{19}{2} a^{5} + \frac{37}{2} a^{4} - 30 a^{3} - \frac{229}{2} a^{2} - 92 a + \frac{67}{2}\) , \( \frac{127}{2} a^{5} + \frac{279}{2} a^{4} - 306 a^{3} - \frac{1501}{2} a^{2} - 201 a + \frac{225}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{3}{2}a^{4}-8a^{3}+\frac{11}{2}a^{2}+9a-\frac{5}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){y}={x}^{3}+\left(-a^{5}+8a^{3}-16a+3\right){x}^{2}+\left(\frac{19}{2}a^{5}+\frac{37}{2}a^{4}-30a^{3}-\frac{229}{2}a^{2}-92a+\frac{67}{2}\right){x}+\frac{127}{2}a^{5}+\frac{279}{2}a^{4}-306a^{3}-\frac{1501}{2}a^{2}-201a+\frac{225}{2}$ |
| 41.1-a2 |
41.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{6} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$4$ |
\( 2 \) |
$1$ |
$8899.576948$ |
3.34691 |
\( \frac{146548489726075}{4750104241} a^{5} + \frac{118704523034197}{4750104241} a^{4} - \frac{1200876493599277}{4750104241} a^{3} - \frac{689860637946669}{4750104241} a^{2} + \frac{2057121192128274}{4750104241} a + \frac{782183193490477}{4750104241} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{3}{2} a^{4} - 8 a^{3} + \frac{11}{2} a^{2} + 9 a - \frac{5}{2}\) , \( -a^{5} + 8 a^{3} - 16 a + 3\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( -3 a^{5} - 4 a^{4} + 35 a^{3} + 8 a^{2} - 82 a + 21\) , \( -11 a^{5} + 2 a^{4} + 83 a^{3} - 11 a^{2} - 149 a + 39\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{3}{2}a^{4}-8a^{3}+\frac{11}{2}a^{2}+9a-\frac{5}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){y}={x}^{3}+\left(-a^{5}+8a^{3}-16a+3\right){x}^{2}+\left(-3a^{5}-4a^{4}+35a^{3}+8a^{2}-82a+21\right){x}-11a^{5}+2a^{4}+83a^{3}-11a^{2}-149a+39$ |
| 41.1-a3 |
41.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{3} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$17799.15389$ |
3.34691 |
\( \frac{66522466629}{68921} a^{5} + \frac{158897720340}{68921} a^{4} - \frac{99678895849}{68921} a^{3} - \frac{336896048130}{68921} a^{2} - \frac{42451186017}{68921} a + \frac{36460530946}{68921} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 2 a^{3} + \frac{3}{2} a^{2} + \frac{1}{2}\) , \( -\frac{3}{2} a^{5} + \frac{1}{2} a^{4} + 9 a^{3} - \frac{1}{2} a^{2} - 11 a - \frac{1}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( 2 a^{4} - 5 a^{3} - 8 a^{2} + 18 a - 2\) , \( -\frac{1}{2} a^{5} - \frac{3}{2} a^{4} + 5 a^{3} + \frac{11}{2} a^{2} - 11 a - \frac{1}{2}\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-2a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-2\right){y}={x}^{3}+\left(-\frac{3}{2}a^{5}+\frac{1}{2}a^{4}+9a^{3}-\frac{1}{2}a^{2}-11a-\frac{1}{2}\right){x}^{2}+\left(2a^{4}-5a^{3}-8a^{2}+18a-2\right){x}-\frac{1}{2}a^{5}-\frac{3}{2}a^{4}+5a^{3}+\frac{11}{2}a^{2}-11a-\frac{1}{2}$ |
| 41.1-a4 |
41.1-a |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{3} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$16$ |
\( 1 \) |
$1$ |
$1112.447118$ |
3.34691 |
\( \frac{702513981298501}{68921} a^{5} + \frac{373138785603258}{68921} a^{4} - \frac{5178206663802839}{68921} a^{3} - \frac{2682827420392867}{68921} a^{2} + \frac{7982907079490886}{68921} a + \frac{2982053773423894}{68921} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 9 a - 2\) , \( -\frac{1}{2} a^{5} + \frac{1}{2} a^{4} + 2 a^{3} - \frac{5}{2} a^{2} + \frac{7}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 2\) , \( -a^{5} + a^{4} + 10 a^{3} - 8 a^{2} - 25 a + 5\) , \( 1198 a^{5} + 1674 a^{4} - 6059 a^{3} - 9672 a^{2} - 279 a + 861\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+9a-2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a^{2}+5a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{5}+\frac{1}{2}a^{4}+2a^{3}-\frac{5}{2}a^{2}+\frac{7}{2}\right){x}^{2}+\left(-a^{5}+a^{4}+10a^{3}-8a^{2}-25a+5\right){x}+1198a^{5}+1674a^{4}-6059a^{3}-9672a^{2}-279a+861$ |
| 41.1-b1 |
41.1-b |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.339963113$ |
$43706.83764$ |
4.19100 |
\( -\frac{1287229}{82} a^{5} - \frac{1854383}{82} a^{4} + \frac{3258948}{41} a^{3} + \frac{10649851}{82} a^{2} + \frac{209624}{41} a - \frac{905757}{82} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{1}{2} a^{2} + 11 a + \frac{1}{2}\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - 3 a^{3} - \frac{7}{2} a^{2} + 3 a + \frac{3}{2}\) , \( a^{5} - 7 a^{3} + 12 a - 1\) , \( 2 a^{5} - 2 a^{4} - 13 a^{3} + 7 a^{2} + 19 a - 1\) , \( \frac{3}{2} a^{5} + \frac{1}{2} a^{4} - 12 a^{3} - \frac{7}{2} a^{2} + 20 a - \frac{3}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{1}{2}a^{2}+11a+\frac{1}{2}\right){x}{y}+\left(a^{5}-7a^{3}+12a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-3a^{3}-\frac{7}{2}a^{2}+3a+\frac{3}{2}\right){x}^{2}+\left(2a^{5}-2a^{4}-13a^{3}+7a^{2}+19a-1\right){x}+\frac{3}{2}a^{5}+\frac{1}{2}a^{4}-12a^{3}-\frac{7}{2}a^{2}+20a-\frac{3}{2}$ |
| 41.1-b2 |
41.1-b |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.679926227$ |
$43706.83764$ |
4.19100 |
\( -\frac{839213287}{3362} a^{5} + \frac{1517618681}{3362} a^{4} + \frac{1492816322}{1681} a^{3} - \frac{4134590273}{3362} a^{2} - \frac{706982195}{1681} a + \frac{619959153}{3362} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a\) , \( -a^{5} + 6 a^{3} - 7 a + 2\) , \( a^{5} - 7 a^{3} + 12 a - 1\) , \( 3 a^{5} + 6 a^{4} - 14 a^{3} - 34 a^{2} - 10 a + 4\) , \( \frac{9}{2} a^{5} + \frac{13}{2} a^{4} - 24 a^{3} - \frac{75}{2} a^{2} + 2 a + \frac{3}{2}\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a\right){x}{y}+\left(a^{5}-7a^{3}+12a-1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-7a+2\right){x}^{2}+\left(3a^{5}+6a^{4}-14a^{3}-34a^{2}-10a+4\right){x}+\frac{9}{2}a^{5}+\frac{13}{2}a^{4}-24a^{3}-\frac{75}{2}a^{2}+2a+\frac{3}{2}$ |
| 41.1-b3 |
41.1-b |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.359852455$ |
$682.9193381$ |
4.19100 |
\( -\frac{18940439315111185}{5651522} a^{5} + \frac{7261746126853253}{5651522} a^{4} + \frac{65490525512845300}{2825761} a^{3} - \frac{28997993510188171}{5651522} a^{2} - \frac{100024019144096981}{2825761} a + \frac{53069582163213439}{5651522} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 2 a^{3} + \frac{3}{2} a^{2} + \frac{1}{2}\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 3\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 15 a - \frac{5}{2}\) , \( \frac{23}{2} a^{5} + \frac{9}{2} a^{4} - 63 a^{3} - \frac{81}{2} a^{2} + 33 a + \frac{1}{2}\) , \( 31 a^{5} + 36 a^{4} - 180 a^{3} - 228 a^{2} + 54 a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-2a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+15a-\frac{5}{2}\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-6a-3\right){x}^{2}+\left(\frac{23}{2}a^{5}+\frac{9}{2}a^{4}-63a^{3}-\frac{81}{2}a^{2}+33a+\frac{1}{2}\right){x}+31a^{5}+36a^{4}-180a^{3}-228a^{2}+54a+2$ |
| 41.1-b4 |
41.1-b |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.339963113$ |
$43706.83764$ |
4.19100 |
\( -\frac{60310865282453}{82} a^{5} + \frac{117358996071893}{82} a^{4} + \frac{96903645608362}{41} a^{3} - \frac{316819458380723}{82} a^{2} - \frac{23460536751851}{41} a + \frac{30994056920195}{82} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 15 a - 2\) , \( -\frac{1}{2} a^{5} - \frac{1}{2} a^{4} + 4 a^{3} + \frac{5}{2} a^{2} - 7 a - \frac{3}{2}\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 12 a - \frac{3}{2}\) , \( -\frac{219}{2} a^{5} - \frac{293}{2} a^{4} + 563 a^{3} + \frac{1691}{2} a^{2} - 27 a - \frac{127}{2}\) , \( -\frac{55}{2} a^{5} - \frac{49}{2} a^{4} + 154 a^{3} + \frac{289}{2} a^{2} - 84 a + \frac{17}{2}\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+3a^{2}+15a-2\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+12a-\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}+4a^{3}+\frac{5}{2}a^{2}-7a-\frac{3}{2}\right){x}^{2}+\left(-\frac{219}{2}a^{5}-\frac{293}{2}a^{4}+563a^{3}+\frac{1691}{2}a^{2}-27a-\frac{127}{2}\right){x}-\frac{55}{2}a^{5}-\frac{49}{2}a^{4}+154a^{3}+\frac{289}{2}a^{2}-84a+\frac{17}{2}$ |
| 41.1-b5 |
41.1-b |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{8} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$2.719704910$ |
$10.67061465$ |
4.19100 |
\( \frac{1128770712339933494546362972619}{15969850458242} a^{5} + \frac{2603418333975769383629211746105}{15969850458242} a^{4} - \frac{948410598208842680820955495964}{7984925229121} a^{3} - \frac{5503635326419307264819960806201}{15969850458242} a^{2} - \frac{138605914341214245871744610849}{7984925229121} a + \frac{489403998074235904223366871955}{15969850458242} \) |
\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 2 a^{3} + \frac{3}{2} a^{2} + \frac{1}{2}\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 3\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 10 a^{3} + \frac{3}{2} a^{2} + 15 a - \frac{5}{2}\) , \( -\frac{7}{2} a^{5} - \frac{31}{2} a^{4} - 23 a^{3} + \frac{29}{2} a^{2} + 33 a - \frac{9}{2}\) , \( -73 a^{5} - 221 a^{4} - 91 a^{3} + 181 a^{2} + 80 a - 34\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-2a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-10a^{3}+\frac{3}{2}a^{2}+15a-\frac{5}{2}\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-6a-3\right){x}^{2}+\left(-\frac{7}{2}a^{5}-\frac{31}{2}a^{4}-23a^{3}+\frac{29}{2}a^{2}+33a-\frac{9}{2}\right){x}-73a^{5}-221a^{4}-91a^{3}+181a^{2}+80a-34$ |
| 41.1-b6 |
41.1-b |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$2.719704910$ |
$10.67061465$ |
4.19100 |
\( -\frac{232348636261786507870011}{3362} a^{5} + \frac{83766254722022207065335}{3362} a^{4} + \frac{798120543266309643988700}{1681} a^{3} - \frac{343127712348189796421879}{3362} a^{2} - \frac{1216065381224906000634255}{1681} a + \frac{644482469234024171763229}{3362} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{3}{2}\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 14 a - 3\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{3}{2}\) , \( -186 a^{5} + 321 a^{4} + 750 a^{3} - 1176 a^{2} - 45 a + 85\) , \( -\frac{7239}{2} a^{5} + \frac{11953}{2} a^{4} + 15298 a^{3} - \frac{43555}{2} a^{2} - 3319 a + \frac{4059}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{3}{2}\right){x}{y}+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{3}{2}\right){y}={x}^{3}+\left(2a^{5}-a^{4}-12a^{3}+3a^{2}+14a-3\right){x}^{2}+\left(-186a^{5}+321a^{4}+750a^{3}-1176a^{2}-45a+85\right){x}-\frac{7239}{2}a^{5}+\frac{11953}{2}a^{4}+15298a^{3}-\frac{43555}{2}a^{2}-3319a+\frac{4059}{2}$ |
| 41.1-c1 |
41.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.010883058$ |
$71850.75697$ |
5.29334 |
\( -\frac{1287229}{82} a^{5} - \frac{1854383}{82} a^{4} + \frac{3258948}{41} a^{3} + \frac{10649851}{82} a^{2} + \frac{209624}{41} a - \frac{905757}{82} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{3}{2}\) , \( \frac{1}{2} a^{5} - \frac{3}{2} a^{4} - 2 a^{3} + \frac{13}{2} a^{2} + a - \frac{7}{2}\) , \( a^{5} - 7 a^{3} - a^{2} + 12 a\) , \( 4 a^{5} - 5 a^{4} - 20 a^{3} + 18 a^{2} + 18 a - 5\) , \( -a^{5} + a^{4} + 5 a^{3} - 7 a - 2\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{3}{2}\right){x}{y}+\left(a^{5}-7a^{3}-a^{2}+12a\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}-\frac{3}{2}a^{4}-2a^{3}+\frac{13}{2}a^{2}+a-\frac{7}{2}\right){x}^{2}+\left(4a^{5}-5a^{4}-20a^{3}+18a^{2}+18a-5\right){x}-a^{5}+a^{4}+5a^{3}-7a-2$ |
| 41.1-c2 |
41.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.010883058$ |
$143701.5139$ |
5.29334 |
\( -\frac{839213287}{3362} a^{5} + \frac{1517618681}{3362} a^{4} + \frac{1492816322}{1681} a^{3} - \frac{4134590273}{3362} a^{2} - \frac{706982195}{1681} a + \frac{619959153}{3362} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( -\frac{1}{2} a^{5} - \frac{1}{2} a^{4} + 4 a^{3} + \frac{7}{2} a^{2} - 8 a - \frac{5}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( 3 a^{5} - 6 a^{3} - 14 a^{2} - 26 a + 14\) , \( -5 a^{5} + 5 a^{4} + 32 a^{3} - 18 a^{2} - 53 a + 12\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}+4a^{3}+\frac{7}{2}a^{2}-8a-\frac{5}{2}\right){x}^{2}+\left(3a^{5}-6a^{3}-14a^{2}-26a+14\right){x}-5a^{5}+5a^{4}+32a^{3}-18a^{2}-53a+12$ |
| 41.1-c3 |
41.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.043532235$ |
$35925.37848$ |
5.29334 |
\( -\frac{18940439315111185}{5651522} a^{5} + \frac{7261746126853253}{5651522} a^{4} + \frac{65490525512845300}{2825761} a^{3} - \frac{28997993510188171}{5651522} a^{2} - \frac{100024019144096981}{2825761} a + \frac{53069582163213439}{5651522} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( -\frac{1}{2} a^{5} - \frac{1}{2} a^{4} + 4 a^{3} + \frac{7}{2} a^{2} - 8 a - \frac{5}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( \frac{61}{2} a^{5} + \frac{75}{2} a^{4} - 146 a^{3} - \frac{463}{2} a^{2} - 26 a + \frac{63}{2}\) , \( \frac{551}{2} a^{5} + \frac{777}{2} a^{4} - 1388 a^{3} - \frac{4489}{2} a^{2} - 92 a + \frac{415}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}+4a^{3}+\frac{7}{2}a^{2}-8a-\frac{5}{2}\right){x}^{2}+\left(\frac{61}{2}a^{5}+\frac{75}{2}a^{4}-146a^{3}-\frac{463}{2}a^{2}-26a+\frac{63}{2}\right){x}+\frac{551}{2}a^{5}+\frac{777}{2}a^{4}-1388a^{3}-\frac{4489}{2}a^{2}-92a+\frac{415}{2}$ |
| 41.1-c4 |
41.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.043532235$ |
$17962.68924$ |
5.29334 |
\( -\frac{60310865282453}{82} a^{5} + \frac{117358996071893}{82} a^{4} + \frac{96903645608362}{41} a^{3} - \frac{316819458380723}{82} a^{2} - \frac{23460536751851}{41} a + \frac{30994056920195}{82} \) |
\( \bigl[a^{5} - 6 a^{3} - a^{2} + 8 a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{5}{2}\) , \( -\frac{45}{2} a^{5} - \frac{69}{2} a^{4} + 113 a^{3} + \frac{395}{2} a^{2} + 16 a - \frac{35}{2}\) , \( -18 a^{5} - 23 a^{4} + 104 a^{3} + 167 a^{2} + 11 a - 17\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-a^{2}+8a+1\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+4a-\frac{5}{2}\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a\right){x}^{2}+\left(-\frac{45}{2}a^{5}-\frac{69}{2}a^{4}+113a^{3}+\frac{395}{2}a^{2}+16a-\frac{35}{2}\right){x}-18a^{5}-23a^{4}+104a^{3}+167a^{2}+11a-17$ |
| 41.1-c5 |
41.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{8} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.174128941$ |
$2245.336155$ |
5.29334 |
\( \frac{1128770712339933494546362972619}{15969850458242} a^{5} + \frac{2603418333975769383629211746105}{15969850458242} a^{4} - \frac{948410598208842680820955495964}{7984925229121} a^{3} - \frac{5503635326419307264819960806201}{15969850458242} a^{2} - \frac{138605914341214245871744610849}{7984925229121} a + \frac{489403998074235904223366871955}{15969850458242} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( -\frac{1}{2} a^{5} - \frac{1}{2} a^{4} + 4 a^{3} + \frac{7}{2} a^{2} - 8 a - \frac{5}{2}\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( \frac{11}{2} a^{5} + \frac{75}{2} a^{4} - 36 a^{3} - \frac{343}{2} a^{2} - 46 a + \frac{43}{2}\) , \( 482 a^{5} + 781 a^{4} - 2501 a^{3} - 4321 a^{2} - 125 a + 408\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{3}{2}a^{2}+11a-\frac{5}{2}\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}+4a^{3}+\frac{7}{2}a^{2}-8a-\frac{5}{2}\right){x}^{2}+\left(\frac{11}{2}a^{5}+\frac{75}{2}a^{4}-36a^{3}-\frac{343}{2}a^{2}-46a+\frac{43}{2}\right){x}+482a^{5}+781a^{4}-2501a^{3}-4321a^{2}-125a+408$ |
| 41.1-c6 |
41.1-c |
$6$ |
$8$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.174128941$ |
$2245.336155$ |
5.29334 |
\( -\frac{232348636261786507870011}{3362} a^{5} + \frac{83766254722022207065335}{3362} a^{4} + \frac{798120543266309643988700}{1681} a^{3} - \frac{343127712348189796421879}{3362} a^{2} - \frac{1216065381224906000634255}{1681} a + \frac{644482469234024171763229}{3362} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{1}{2} a^{2} + 12 a + \frac{1}{2}\) , \( -a^{5} + 7 a^{3} + a^{2} - 11 a\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{5}{2}\) , \( -\frac{157}{2} a^{5} + \frac{333}{2} a^{4} + 285 a^{3} - \frac{1293}{2} a^{2} + 101 a + \frac{245}{2}\) , \( 2715 a^{5} - 1425 a^{4} - 15805 a^{3} + 2155 a^{2} + 17458 a + 5311\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{1}{2}a^{2}+12a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+4a-\frac{5}{2}\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+a^{2}-11a\right){x}^{2}+\left(-\frac{157}{2}a^{5}+\frac{333}{2}a^{4}+285a^{3}-\frac{1293}{2}a^{2}+101a+\frac{245}{2}\right){x}+2715a^{5}-1425a^{4}-15805a^{3}+2155a^{2}+17458a+5311$ |
| 41.1-d1 |
41.1-d |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{12} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 2^{2} \cdot 3 \) |
$0.108504227$ |
$491.4048212$ |
2.88751 |
\( -\frac{4198436361667110996600488530}{22563490300366186081} a^{5} - \frac{5844757786544332783449381171}{22563490300366186081} a^{4} + \frac{21252423766059100218293843129}{22563490300366186081} a^{3} + \frac{33784506632375941559480720450}{22563490300366186081} a^{2} + \frac{849487561148946913710553326}{22563490300366186081} a - \frac{3015806472984505420487097371}{22563490300366186081} \) |
\( \bigl[\frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{1}{2} a^{2} + 11 a + \frac{1}{2}\) , \( -\frac{1}{2} a^{5} + \frac{1}{2} a^{4} + 3 a^{3} - \frac{3}{2} a^{2} - 4 a + \frac{1}{2}\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{3}{2} a^{2} + 4 a - \frac{1}{2}\) , \( -3 a^{5} - 6 a^{4} + 4 a^{3} - 6 a^{2} - 23 a + 7\) , \( -\frac{57}{2} a^{5} - \frac{125}{2} a^{4} + 28 a^{3} + \frac{147}{2} a^{2} - 25 a + \frac{3}{2}\bigr] \) |
${y}^2+\left(\frac{3}{2}a^{5}-\frac{1}{2}a^{4}-9a^{3}+\frac{1}{2}a^{2}+11a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{3}{2}a^{2}+4a-\frac{1}{2}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{5}+\frac{1}{2}a^{4}+3a^{3}-\frac{3}{2}a^{2}-4a+\frac{1}{2}\right){x}^{2}+\left(-3a^{5}-6a^{4}+4a^{3}-6a^{2}-23a+7\right){x}-\frac{57}{2}a^{5}-\frac{125}{2}a^{4}+28a^{3}+\frac{147}{2}a^{2}-25a+\frac{3}{2}$ |
| 41.1-d2 |
41.1-d |
$4$ |
$4$ |
6.6.1767625.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{6} \) |
$161.89457$ |
$(a^5-a^4-5a^3+3a^2+5a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.054252113$ |
$31449.90856$ |
2.88751 |
\( \frac{146548489726075}{4750104241} a^{5} + \frac{118704523034197}{4750104241} a^{4} - \frac{1200876493599277}{4750104241} a^{3} - \frac{689860637946669}{4750104241} a^{2} + \frac{2057121192128274}{4750104241} a + \frac{782183193490477}{4750104241} \) |
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 16 a - 3\) , \( \frac{1}{2} a^{5} - \frac{3}{2} a^{4} - 2 a^{3} + \frac{13}{2} a^{2} - \frac{7}{2}\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{3}{2}\) , \( -6 a^{5} + 5 a^{4} + 41 a^{3} - 24 a^{2} - 73 a + 23\) , \( -\frac{19}{2} a^{5} + \frac{21}{2} a^{4} + 70 a^{3} - \frac{99}{2} a^{2} - 131 a + \frac{73}{2}\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+3a^{2}+16a-3\right){x}{y}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-3a^{3}+\frac{5}{2}a^{2}+4a-\frac{3}{2}\right){y}={x}^{3}+\left(\frac{1}{2}a^{5}-\frac{3}{2}a^{4}-2a^{3}+\frac{13}{2}a^{2}-\frac{7}{2}\right){x}^{2}+\left(-6a^{5}+5a^{4}+41a^{3}-24a^{2}-73a+23\right){x}-\frac{19}{2}a^{5}+\frac{21}{2}a^{4}+70a^{3}-\frac{99}{2}a^{2}-131a+\frac{73}{2}$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
