| 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 |
| 5.1-a1 |
5.1-a |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5^{15} \) |
$113.83972$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1682.101420$ |
1.50989 |
\( -\frac{584205938671037576}{390625} a^{5} + \frac{127830640643771423}{390625} a^{4} + \frac{4061470830963324523}{390625} a^{3} + \frac{279717696988069228}{390625} a^{2} - \frac{1297494123233689326}{78125} a - \frac{2669912142068228202}{390625} \) |
\( \bigl[a^{5} - 7 a^{3} - a^{2} + 12 a + 4\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 30 a + 11\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( 23 a^{5} - 29 a^{4} - 127 a^{3} + 109 a^{2} + 123 a + 24\) , \( 95 a^{5} - 121 a^{4} - 514 a^{3} + 463 a^{2} + 467 a + 73\bigr] \) |
${y}^2+\left(a^{5}-7a^{3}-a^{2}+12a+4\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-20a^{3}+5a^{2}+30a+11\right){x}^{2}+\left(23a^{5}-29a^{4}-127a^{3}+109a^{2}+123a+24\right){x}+95a^{5}-121a^{4}-514a^{3}+463a^{2}+467a+73$ |
| 5.1-a2 |
5.1-a |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$113.83972$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1682.101420$ |
1.50989 |
\( \frac{1332544}{5} a^{5} + \frac{2260678}{5} a^{4} - \frac{5421687}{5} a^{3} - \frac{11771837}{5} a^{2} - 1128428 a - \frac{732232}{5} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 9\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 18 a - 6\) , \( -2 a^{5} + 4 a^{4} + 18 a^{3} - 10 a^{2} - 35 a - 11\) , \( a^{5} + 4 a^{4} + a^{3} - 12 a^{2} - 11 a - 3\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-9\right){x}{y}+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-18a-6\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-4\right){x}^{2}+\left(-2a^{5}+4a^{4}+18a^{3}-10a^{2}-35a-11\right){x}+a^{5}+4a^{4}+a^{3}-12a^{2}-11a-3$ |
| 5.1-a3 |
5.1-a |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5^{5} \) |
$113.83972$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1682.101420$ |
1.50989 |
\( -\frac{13681459876}{125} a^{5} - \frac{36187576902}{125} a^{4} + \frac{25331233773}{125} a^{3} + \frac{99876956003}{125} a^{2} + \frac{10695502109}{25} a + \frac{7259236048}{125} \) |
\( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -2 a^{5} + 13 a^{3} + 3 a^{2} - 19 a - 7\) , \( a^{2} + a - 2\) , \( 20 a^{5} - 9 a^{4} - 145 a^{3} + 8 a^{2} + 244 a + 98\) , \( 13 a^{5} - 7 a^{4} - 106 a^{3} - 6 a^{2} + 200 a + 114\bigr] \) |
${y}^2+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-2a^{5}+13a^{3}+3a^{2}-19a-7\right){x}^{2}+\left(20a^{5}-9a^{4}-145a^{3}+8a^{2}+244a+98\right){x}+13a^{5}-7a^{4}-106a^{3}-6a^{2}+200a+114$ |
| 5.1-a4 |
5.1-a |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$113.83972$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1682.101420$ |
1.50989 |
\( \frac{3288568389824}{25} a^{5} - \frac{1515811489972}{25} a^{4} - \frac{22321293042632}{25} a^{3} + \frac{3711500587103}{25} a^{2} + \frac{6892701907756}{5} a + \frac{7134572445643}{25} \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 42 a - 15\) , \( 5 a^{5} - 2 a^{4} - 34 a^{3} + 3 a^{2} + 53 a + 15\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( 12 a^{5} - 2 a^{4} - 86 a^{3} - 12 a^{2} + 146 a + 71\) , \( 80 a^{5} + 15 a^{4} - 507 a^{3} - 179 a^{2} + 627 a + 273\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-42a-15\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-30a-12\right){y}={x}^{3}+\left(5a^{5}-2a^{4}-34a^{3}+3a^{2}+53a+15\right){x}^{2}+\left(12a^{5}-2a^{4}-86a^{3}-12a^{2}+146a+71\right){x}+80a^{5}+15a^{4}-507a^{3}-179a^{2}+627a+273$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
5.1 |
\( 5 \) |
\( 5^{13} \) |
$113.83972$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1307.429678$ |
1.17357 |
\( \frac{1376405109}{78125} a^{5} - \frac{1325860482}{78125} a^{4} - \frac{7597745332}{78125} a^{3} + \frac{2698464798}{78125} a^{2} + \frac{2247897599}{15625} a + \frac{2321410818}{78125} \) |
\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( 4 a^{5} - a^{4} - 28 a^{3} - a^{2} + 44 a + 15\) , \( a^{2} + a - 2\) , \( 27 a^{5} - 5 a^{4} - 189 a^{3} - 19 a^{2} + 305 a + 129\) , \( 54 a^{5} - 13 a^{4} - 375 a^{3} - 21 a^{2} + 598 a + 243\bigr] \) |
${y}^2+\left(-3a^{5}+a^{4}+20a^{3}-29a-12\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(4a^{5}-a^{4}-28a^{3}-a^{2}+44a+15\right){x}^{2}+\left(27a^{5}-5a^{4}-189a^{3}-19a^{2}+305a+129\right){x}+54a^{5}-13a^{4}-375a^{3}-21a^{2}+598a+243$ |
| 9.1-a1 |
9.1-a |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1226.536094$ |
1.10096 |
\( \frac{79572442844}{27} a^{5} + \frac{179028656408}{27} a^{4} - \frac{154197900412}{27} a^{3} - \frac{506013769217}{27} a^{2} - \frac{263202231980}{27} a - \frac{35350337779}{27} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 5\) , \( 4 a^{5} - 2 a^{4} - 27 a^{3} + 3 a^{2} + 41 a + 15\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( 18 a^{5} + 6 a^{4} - 105 a^{3} - 50 a^{2} + 97 a + 43\) , \( 47 a^{5} + 62 a^{4} - 218 a^{3} - 338 a^{2} - 56 a + 22\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-11a-5\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-27a^{3}+3a^{2}+41a+15\right){x}^{2}+\left(18a^{5}+6a^{4}-105a^{3}-50a^{2}+97a+43\right){x}+47a^{5}+62a^{4}-218a^{3}-338a^{2}-56a+22$ |
| 9.1-a2 |
9.1-a |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{30} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1226.536094$ |
1.10096 |
\( -\frac{47946476284126}{14348907} a^{5} - \frac{21211156063675}{14348907} a^{4} + \frac{404669473071680}{14348907} a^{3} + \frac{98469557612671}{14348907} a^{2} - \frac{670666419604364}{14348907} a - \frac{290449774050121}{14348907} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 10\) , \( -a^{5} + a^{4} + 7 a^{3} - 4 a^{2} - 11 a - 1\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( -77 a^{5} + 37 a^{4} + 522 a^{3} - 95 a^{2} - 804 a - 158\) , \( -354 a^{5} + 162 a^{4} + 2399 a^{3} - 399 a^{2} - 3697 a - 758\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-10\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-12\right){y}={x}^{3}+\left(-a^{5}+a^{4}+7a^{3}-4a^{2}-11a-1\right){x}^{2}+\left(-77a^{5}+37a^{4}+522a^{3}-95a^{2}-804a-158\right){x}-354a^{5}+162a^{4}+2399a^{3}-399a^{2}-3697a-758$ |
| 9.1-b1 |
9.1-b |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.016952447$ |
$26721.26522$ |
2.43968 |
\( -\frac{961893898216}{3} a^{5} + \frac{211583061698}{3} a^{4} + \frac{6688850789906}{3} a^{3} + \frac{455704107955}{3} a^{2} - \frac{10690384702193}{3} a - \frac{4398914300311}{3} \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 15\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 2\) , \( 22 a^{5} + 2 a^{4} - 126 a^{3} - 50 a^{2} + 137 a + 62\) , \( -20 a^{5} - 105 a^{4} + 48 a^{3} + 445 a^{2} + 407 a + 102\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-41a-15\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+1\right){x}^{2}+\left(22a^{5}+2a^{4}-126a^{3}-50a^{2}+137a+62\right){x}-20a^{5}-105a^{4}+48a^{3}+445a^{2}+407a+102$ |
| 9.1-b2 |
9.1-b |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.003390489$ |
$26721.26522$ |
2.43968 |
\( \frac{17522450}{243} a^{5} + \frac{39783650}{243} a^{4} - \frac{33141304}{243} a^{3} - \frac{112323782}{243} a^{2} - \frac{60359501}{243} a - \frac{8259061}{243} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 31 a - 10\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 11\) , \( -8 a^{5} + 2 a^{4} + 54 a^{3} + a^{2} - 82 a - 26\) , \( 2 a^{5} - 14 a^{3} - 4 a^{2} + 22 a + 14\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-31a-10\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-30a-11\right){y}={x}^{3}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-12\right){x}^{2}+\left(-8a^{5}+2a^{4}+54a^{3}+a^{2}-82a-26\right){x}+2a^{5}-14a^{3}-4a^{2}+22a+14$ |
| 11.1-a1 |
11.1-a |
$2$ |
$3$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$121.57073$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.003372711$ |
$53864.21374$ |
2.93525 |
\( \frac{6472064061}{1331} a^{5} + \frac{11206126614}{1331} a^{4} - \frac{25965665105}{1331} a^{3} - \frac{58239257238}{1331} a^{2} - \frac{29240306026}{1331} a - \frac{4017210022}{1331} \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 15\) , \( 3 a^{5} - a^{4} - 20 a^{3} + 29 a + 13\) , \( 0\) , \( 36 a^{5} - 8 a^{4} - 244 a^{3} - 19 a^{2} + 377 a + 180\) , \( 111 a^{5} - 30 a^{4} - 755 a^{3} - 8 a^{2} + 1174 a + 439\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-41a-15\right){x}{y}={x}^{3}+\left(3a^{5}-a^{4}-20a^{3}+29a+13\right){x}^{2}+\left(36a^{5}-8a^{4}-244a^{3}-19a^{2}+377a+180\right){x}+111a^{5}-30a^{4}-755a^{3}-8a^{2}+1174a+439$ |
| 11.1-a2 |
11.1-a |
$2$ |
$3$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$121.57073$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.010118134$ |
$53864.21374$ |
2.93525 |
\( -\frac{20305}{11} a^{5} + \frac{37335}{11} a^{4} + \frac{90480}{11} a^{3} - \frac{154151}{11} a^{2} - \frac{23691}{11} a + \frac{14376}{11} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( a^{3} + a^{2} - 3 a - 4\) , \( -2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 9\) , \( -4 a^{5} + 2 a^{4} + 28 a^{3} - 2 a^{2} - 45 a - 17\) , \( -2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 8\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-10\right){x}{y}+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-9\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-4\right){x}^{2}+\left(-4a^{5}+2a^{4}+28a^{3}-2a^{2}-45a-17\right){x}-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-8$ |
| 25.1-a1 |
25.1-a |
$4$ |
$6$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$130.17912$ |
$(a^3+a^2-4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4473.753968$ |
1.00393 |
\( -\frac{741965922311}{25} a^{5} + \frac{342221919648}{25} a^{4} + \frac{5035970205644}{25} a^{3} - \frac{838880007087}{25} a^{2} - \frac{7775063007306}{25} a - \frac{1607474967103}{25} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( -4 a^{5} + a^{4} + 27 a^{3} + a^{2} - 40 a - 14\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 18 a - 5\) , \( -11 a^{5} + 3 a^{4} + 74 a^{3} + 2 a^{2} - 110 a - 42\) , \( -13 a^{5} + 5 a^{4} + 93 a^{3} - 3 a^{2} - 158 a - 64\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-10\right){x}{y}+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-18a-5\right){y}={x}^{3}+\left(-4a^{5}+a^{4}+27a^{3}+a^{2}-40a-14\right){x}^{2}+\left(-11a^{5}+3a^{4}+74a^{3}+2a^{2}-110a-42\right){x}-13a^{5}+5a^{4}+93a^{3}-3a^{2}-158a-64$ |
| 25.1-a2 |
25.1-a |
$4$ |
$6$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{36} \) |
$130.17912$ |
$(a^3+a^2-4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$559.2192461$ |
1.00393 |
\( \frac{28838507429}{1953125} a^{5} + \frac{224441782888}{1953125} a^{4} - \frac{713836853429}{1953125} a^{3} - \frac{568897728419}{1953125} a^{2} + \frac{1302159264183}{1953125} a + \frac{671649770161}{1953125} \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 15\) , \( 4 a^{5} - a^{4} - 27 a^{3} - a^{2} + 40 a + 15\) , \( a^{5} - 7 a^{3} - a^{2} + 11 a + 4\) , \( -116 a^{5} + 158 a^{4} + 600 a^{3} - 625 a^{2} - 463 a - 37\) , \( -1944 a^{5} + 2222 a^{4} + 10827 a^{3} - 8233 a^{2} - 10826 a - 2325\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-41a-15\right){x}{y}+\left(a^{5}-7a^{3}-a^{2}+11a+4\right){y}={x}^{3}+\left(4a^{5}-a^{4}-27a^{3}-a^{2}+40a+15\right){x}^{2}+\left(-116a^{5}+158a^{4}+600a^{3}-625a^{2}-463a-37\right){x}-1944a^{5}+2222a^{4}+10827a^{3}-8233a^{2}-10826a-2325$ |
| 25.1-a3 |
25.1-a |
$4$ |
$6$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{18} \) |
$130.17912$ |
$(a^3+a^2-4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$4473.753968$ |
1.00393 |
\( \frac{101075266643}{3125} a^{5} - \frac{134283523372}{3125} a^{4} - \frac{550130346521}{3125} a^{3} + \frac{519049318449}{3125} a^{2} + \frac{103850128721}{625} a + \frac{83367248738}{3125} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -a^{5} + 8 a^{3} + a^{2} - 14 a - 4\) , \( a^{5} - 7 a^{3} - a^{2} + 12 a + 3\) , \( 210 a^{5} - 97 a^{4} - 1422 a^{3} + 239 a^{2} + 2190 a + 453\) , \( -1093 a^{5} + 504 a^{4} + 7417 a^{3} - 1232 a^{2} - 11453 a - 2371\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){x}{y}+\left(a^{5}-7a^{3}-a^{2}+12a+3\right){y}={x}^{3}+\left(-a^{5}+8a^{3}+a^{2}-14a-4\right){x}^{2}+\left(210a^{5}-97a^{4}-1422a^{3}+239a^{2}+2190a+453\right){x}-1093a^{5}+504a^{4}+7417a^{3}-1232a^{2}-11453a-2371$ |
| 25.1-a4 |
25.1-a |
$4$ |
$6$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{12} \) |
$130.17912$ |
$(a^3+a^2-4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$559.2192461$ |
1.00393 |
\( \frac{375754911248012997}{125} a^{5} - \frac{82219231758187987}{125} a^{4} - \frac{2612293806972726921}{125} a^{3} - \frac{179911495733656137}{125} a^{2} + \frac{4172670325015816079}{125} a + \frac{1717258379846324351}{125} \) |
\( \bigl[a^{2} - 2\) , \( -a^{5} + 7 a^{3} + a^{2} - 12 a - 4\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 19\) , \( -70 a^{5} + 31 a^{4} + 394 a^{3} - 64 a^{2} - 360 a - 116\) , \( 203 a^{5} - 178 a^{4} - 975 a^{3} + 640 a^{2} + 347 a - 60\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-19\right){y}={x}^{3}+\left(-a^{5}+7a^{3}+a^{2}-12a-4\right){x}^{2}+\left(-70a^{5}+31a^{4}+394a^{3}-64a^{2}-360a-116\right){x}+203a^{5}-178a^{4}-975a^{3}+640a^{2}+347a-60$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{3} \) |
$130.17912$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.008964453$ |
$31253.00479$ |
3.01779 |
\( -2708 a^{5} + 733 a^{4} + 12894 a^{3} - 3948 a^{2} - 9886 a - 1842 \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 2 a^{2} + 20 a + 5\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 19\) , \( -6 a^{5} + 2 a^{4} + 40 a^{3} - 60 a - 21\) , \( -5 a^{5} + a^{4} + 35 a^{3} + 3 a^{2} - 55 a - 24\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-19\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+2a^{2}+20a+5\right){x}^{2}+\left(-6a^{5}+2a^{4}+40a^{3}-60a-21\right){x}-5a^{5}+a^{4}+35a^{3}+3a^{2}-55a-24$ |
| 25.2-b1 |
25.2-b |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{21} \) |
$130.17912$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$40.42142472$ |
1.81415 |
\( -\frac{584205938671037576}{390625} a^{5} + \frac{127830640643771423}{390625} a^{4} + \frac{4061470830963324523}{390625} a^{3} + \frac{279717696988069228}{390625} a^{2} - \frac{1297494123233689326}{78125} a - \frac{2669912142068228202}{390625} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -6 a^{5} + 2 a^{4} + 41 a^{3} - a^{2} - 65 a - 23\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( -45 a^{5} + 22 a^{4} + 303 a^{3} - 59 a^{2} - 463 a - 84\) , \( -5610 a^{5} + 2584 a^{4} + 38079 a^{3} - 6320 a^{2} - 58796 a - 12189\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-29a-12\right){y}={x}^{3}+\left(-6a^{5}+2a^{4}+41a^{3}-a^{2}-65a-23\right){x}^{2}+\left(-45a^{5}+22a^{4}+303a^{3}-59a^{2}-463a-84\right){x}-5610a^{5}+2584a^{4}+38079a^{3}-6320a^{2}-58796a-12189$ |
| 25.2-b2 |
25.2-b |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{7} \) |
$130.17912$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$25263.39045$ |
1.81415 |
\( \frac{1332544}{5} a^{5} + \frac{2260678}{5} a^{4} - \frac{5421687}{5} a^{3} - \frac{11771837}{5} a^{2} - 1128428 a - \frac{732232}{5} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 6\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -5 a^{5} + a^{4} + 36 a^{3} + 3 a^{2} - 62 a - 25\) , \( -6 a^{5} + a^{4} + 41 a^{3} + 4 a^{2} - 64 a - 27\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-11a-6\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+20a^{3}-30a-12\right){x}^{2}+\left(-5a^{5}+a^{4}+36a^{3}+3a^{2}-62a-25\right){x}-6a^{5}+a^{4}+41a^{3}+4a^{2}-64a-27$ |
| 25.2-b3 |
25.2-b |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{11} \) |
$130.17912$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$40.42142472$ |
1.81415 |
\( -\frac{13681459876}{125} a^{5} - \frac{36187576902}{125} a^{4} + \frac{25331233773}{125} a^{3} + \frac{99876956003}{125} a^{2} + \frac{10695502109}{25} a + \frac{7259236048}{125} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( 4 a^{5} - a^{4} - 28 a^{3} - a^{2} + 45 a + 16\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 18\) , \( 4 a^{5} - a^{4} - 48 a^{3} - 8 a^{2} + 139 a + 64\) , \( 5 a^{5} + 11 a^{4} - 60 a^{3} - 66 a^{2} + 162 a + 80\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-10\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-18\right){y}={x}^{3}+\left(4a^{5}-a^{4}-28a^{3}-a^{2}+45a+16\right){x}^{2}+\left(4a^{5}-a^{4}-48a^{3}-8a^{2}+139a+64\right){x}+5a^{5}+11a^{4}-60a^{3}-66a^{2}+162a+80$ |
| 25.2-b4 |
25.2-b |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{9} \) |
$130.17912$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$25263.39045$ |
1.81415 |
\( \frac{3288568389824}{25} a^{5} - \frac{1515811489972}{25} a^{4} - \frac{22321293042632}{25} a^{3} + \frac{3711500587103}{25} a^{2} + \frac{6892701907756}{5} a + \frac{7134572445643}{25} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 10\) , \( -6 a^{5} + 2 a^{4} + 41 a^{3} - a^{2} - 65 a - 21\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( -2 a^{5} - 3 a^{4} + 18 a^{3} + 16 a^{2} - 36 a - 16\) , \( -2 a^{5} - 2 a^{4} + 17 a^{3} + 16 a^{2} - 40 a - 20\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-10\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-29a-12\right){y}={x}^{3}+\left(-6a^{5}+2a^{4}+41a^{3}-a^{2}-65a-21\right){x}^{2}+\left(-2a^{5}-3a^{4}+18a^{3}+16a^{2}-36a-16\right){x}-2a^{5}-2a^{4}+17a^{3}+16a^{2}-40a-20$ |
| 25.2-c1 |
25.2-c |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{19} \) |
$130.17912$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$808.4057645$ |
1.45128 |
\( \frac{1376405109}{78125} a^{5} - \frac{1325860482}{78125} a^{4} - \frac{7597745332}{78125} a^{3} + \frac{2698464798}{78125} a^{2} + \frac{2247897599}{15625} a + \frac{2321410818}{78125} \) |
\( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 18 a - 6\) , \( -a^{2} + a + 2\) , \( -a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 5\) , \( 26 a^{5} - 12 a^{4} - 176 a^{3} + 29 a^{2} + 270 a + 59\) , \( -51 a^{5} + 24 a^{4} + 346 a^{3} - 61 a^{2} - 534 a - 106\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-18a-6\right){x}{y}+\left(-a^{5}+7a^{3}+2a^{2}-11a-5\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(26a^{5}-12a^{4}-176a^{3}+29a^{2}+270a+59\right){x}-51a^{5}+24a^{4}+346a^{3}-61a^{2}-534a-106$ |
| 25.2-d1 |
25.2-d |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{9} \) |
$130.17912$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.020207192$ |
$12955.98893$ |
2.82001 |
\( -2708 a^{5} + 733 a^{4} + 12894 a^{3} - 3948 a^{2} - 9886 a - 1842 \) |
\( \bigl[a^{2} + a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -8 a^{5} + 3 a^{4} + 53 a^{3} - 5 a^{2} - 79 a - 22\) , \( -8 a^{5} + 3 a^{4} + 54 a^{3} - 4 a^{2} - 83 a - 27\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}^{2}+\left(-8a^{5}+3a^{4}+53a^{3}-5a^{2}-79a-22\right){x}-8a^{5}+3a^{4}+54a^{3}-4a^{2}-83a-27$ |
| 29.1-a1 |
29.1-a |
$2$ |
$7$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$131.79921$ |
$(a^4-a^3-5a^2+3a+4)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$0.220715821$ |
$105599.3722$ |
2.56178 |
\( -\frac{808367}{29} a^{5} - \frac{232409}{29} a^{4} + \frac{3911969}{29} a^{3} + \frac{1920337}{29} a^{2} - \frac{569967}{29} a - \frac{293942}{29} \) |
\( \bigl[a^{2} - 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 7 a - 2\) , \( -4 a^{5} + 2 a^{4} + 26 a^{3} - 5 a^{2} - 38 a - 9\) , \( -23 a^{5} + 11 a^{4} + 155 a^{3} - 28 a^{2} - 237 a - 49\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-7a-2\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-5\right){x}^{2}+\left(-4a^{5}+2a^{4}+26a^{3}-5a^{2}-38a-9\right){x}-23a^{5}+11a^{4}+155a^{3}-28a^{2}-237a-49$ |
| 29.1-a2 |
29.1-a |
$2$ |
$7$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{7} \) |
$131.79921$ |
$(a^4-a^3-5a^2+3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 7 \) |
$1.545010749$ |
$0.897579853$ |
2.56178 |
\( \frac{13815841607213083975511386207}{17249876309} a^{5} - \frac{28062038812038612265502450888}{17249876309} a^{4} - \frac{39710623624428834678366798314}{17249876309} a^{3} + \frac{53026981056198164144695142492}{17249876309} a^{2} + \frac{44263596385560929969398311274}{17249876309} a + \frac{6801758503148238763013009216}{17249876309} \) |
\( \bigl[a^{2} - 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 7 a - 2\) , \( 1531 a^{5} - 743 a^{4} - 10369 a^{3} + 1820 a^{2} + 16027 a + 3286\) , \( 33441 a^{5} - 15713 a^{4} - 226728 a^{3} + 38407 a^{2} + 350175 a + 72382\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-7a-2\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-5\right){x}^{2}+\left(1531a^{5}-743a^{4}-10369a^{3}+1820a^{2}+16027a+3286\right){x}+33441a^{5}-15713a^{4}-226728a^{3}+38407a^{2}+350175a+72382$ |
| 41.1-a1 |
41.1-a |
$2$ |
$7$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{7} \) |
$135.65786$ |
$(a^4+a^3-4a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.553575460$ |
1.19306 |
\( \frac{300039257776916723031380}{194754273881} a^{5} - \frac{135201991016220514678646}{194754273881} a^{4} - \frac{1435403563400771691241019}{194754273881} a^{3} + \frac{343098620572538429827465}{194754273881} a^{2} + \frac{360645134275870330036563}{194754273881} a - \frac{34885214721449234564804}{194754273881} \) |
\( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a + 1\) , \( -4178 a^{5} + 5149 a^{4} + 22801 a^{3} - 19626 a^{2} - 21217 a - 3693\) , \( -269508 a^{5} + 337696 a^{4} + 1461510 a^{3} - 1289635 a^{2} - 1338554 a - 220717\bigr] \) |
${y}^2+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-4178a^{5}+5149a^{4}+22801a^{3}-19626a^{2}-21217a-3693\right){x}-269508a^{5}+337696a^{4}+1461510a^{3}-1289635a^{2}-1338554a-220717$ |
| 41.1-a2 |
41.1-a |
$2$ |
$7$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$135.65786$ |
$(a^4+a^3-4a^2-3a+1)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$65127.59936$ |
1.19306 |
\( \frac{29512728}{41} a^{5} - \frac{13366180}{41} a^{4} - \frac{200948098}{41} a^{3} + \frac{33043551}{41} a^{2} + \frac{310256233}{41} a + \frac{64285367}{41} \) |
\( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a + 1\) , \( 42 a^{5} - a^{4} - 304 a^{3} - 61 a^{2} + 513 a + 222\) , \( 107 a^{5} - 33 a^{4} - 729 a^{3} - 2 a^{2} + 1128 a + 453\bigr] \) |
${y}^2+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(42a^{5}-a^{4}-304a^{3}-61a^{2}+513a+222\right){x}+107a^{5}-33a^{4}-729a^{3}-2a^{2}+1128a+453$ |
| 45.1-a1 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{10} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$0.156385680$ |
$7827.540648$ |
3.29637 |
\( -\frac{4702123576857616}{9375} a^{5} + \frac{722454184206072}{3125} a^{4} + \frac{6383172803344204}{1875} a^{3} - \frac{5306831170078837}{9375} a^{2} - \frac{49277299547829394}{9375} a - \frac{27203459111363}{25} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( -3 a^{5} + a^{4} + 21 a^{3} - a^{2} - 34 a - 9\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( -54 a^{5} + 50 a^{4} + 320 a^{3} - 170 a^{2} - 377 a - 100\) , \( 194 a^{5} - 228 a^{4} - 1073 a^{3} + 851 a^{2} + 1049 a + 215\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}-a^{2}-34a-9\right){x}^{2}+\left(-54a^{5}+50a^{4}+320a^{3}-170a^{2}-377a-100\right){x}+194a^{5}-228a^{4}-1073a^{3}+851a^{2}+1049a+215$ |
| 45.1-a2 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{20} \cdot 5^{4} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.062554272$ |
$1956.885162$ |
3.29637 |
\( \frac{132995277174727124}{1476225} a^{5} + \frac{299238637140317522}{1476225} a^{4} - \frac{257681353571429176}{1476225} a^{3} - \frac{845771537745059027}{1476225} a^{2} - \frac{440033964830611637}{1476225} a - \frac{59108871769893511}{1476225} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 10\) , \( a^{3} - 4 a - 2\) , \( a + 1\) , \( 11 a^{5} - a^{4} - 54 a^{3} - 21 a^{2} + 43 a + 20\) , \( -a^{5} + 31 a^{4} - 105 a^{2} - 82 a - 17\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-10\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(11a^{5}-a^{4}-54a^{3}-21a^{2}+43a+20\right){x}-a^{5}+31a^{4}-105a^{2}-82a-17$ |
| 45.1-a3 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{20} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$0.312771361$ |
$1956.885162$ |
3.29637 |
\( -\frac{1170502190383485568}{87890625} a^{5} + \frac{2369444969907304208}{87890625} a^{4} + \frac{672172040852308774}{17578125} a^{3} - \frac{4461956553521766476}{87890625} a^{2} - \frac{3714094569105967907}{87890625} a - \frac{113245323031240913}{17578125} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( -3 a^{5} + a^{4} + 21 a^{3} - a^{2} - 34 a - 9\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( -224 a^{5} + 85 a^{4} + 1510 a^{3} - 80 a^{2} - 2302 a - 895\) , \( 1545 a^{5} - 573 a^{4} - 10410 a^{3} + 444 a^{2} + 15839 a + 6248\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){y}={x}^{3}+\left(-3a^{5}+a^{4}+21a^{3}-a^{2}-34a-9\right){x}^{2}+\left(-224a^{5}+85a^{4}+1510a^{3}-80a^{2}-2302a-895\right){x}+1545a^{5}-573a^{4}-10410a^{3}+444a^{2}+15839a+6248$ |
| 45.1-a4 |
45.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \cdot 5 \) |
$0.031277136$ |
$7827.540648$ |
3.29637 |
\( -\frac{4772564}{1215} a^{5} - \frac{11376679}{81} a^{4} - \frac{145900826}{1215} a^{3} + \frac{541506817}{1215} a^{2} + \frac{379895386}{1215} a + \frac{18685933}{405} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 10\) , \( a^{3} - 4 a - 2\) , \( a + 1\) , \( 6 a^{5} - a^{4} - 44 a^{3} - a^{2} + 73 a + 30\) , \( 5 a^{5} + 2 a^{4} - 31 a^{3} - 14 a^{2} + 35 a + 16\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-10\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(6a^{5}-a^{4}-44a^{3}-a^{2}+73a+30\right){x}+5a^{5}+2a^{4}-31a^{3}-14a^{2}+35a+16$ |
| 45.1-b1 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$962.3881611$ |
1.72772 |
\( -\frac{7123542098130361856}{15} a^{5} + \frac{1094487484828556022}{5} a^{4} + \frac{9670258293892248323}{3} a^{3} - \frac{8039599121866810022}{15} a^{2} - \frac{74653016232684779294}{15} a - 1030302127993585170 \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 13\) , \( a^{5} - 7 a^{3} - a^{2} + 11 a + 4\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( 686 a^{5} - 226 a^{4} - 4542 a^{3} + 352 a^{2} + 6572 a + 1376\) , \( 8264 a^{5} - 4931 a^{4} - 57506 a^{3} + 14498 a^{2} + 94248 a + 19342\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-13\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){y}={x}^{3}+\left(a^{5}-7a^{3}-a^{2}+11a+4\right){x}^{2}+\left(686a^{5}-226a^{4}-4542a^{3}+352a^{2}+6572a+1376\right){x}+8264a^{5}-4931a^{4}-57506a^{3}+14498a^{2}+94248a+19342$ |
| 45.1-b2 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$60.14926007$ |
1.72772 |
\( \frac{974480916610807874048}{50625} a^{5} + \frac{2192578635875788926082}{50625} a^{4} - \frac{377615335888840389773}{10125} a^{3} - \frac{2065709568086390135938}{16875} a^{2} - \frac{358246336659862446862}{5625} a - \frac{86620748507289493126}{10125} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( 132 a^{5} - 252 a^{4} - 589 a^{3} + 1066 a^{2} + 151 a - 199\) , \( -9857 a^{5} + 12020 a^{4} + 53933 a^{3} - 45477 a^{2} - 50903 a - 9271\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-10\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-12\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){x}^{2}+\left(132a^{5}-252a^{4}-589a^{3}+1066a^{2}+151a-199\right){x}-9857a^{5}+12020a^{4}+53933a^{3}-45477a^{2}-50903a-9271$ |
| 45.1-b3 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3849.552644$ |
1.72772 |
\( -\frac{111388131328}{225} a^{5} + \frac{62867896343}{225} a^{4} + \frac{155339260534}{45} a^{3} - \frac{157390329971}{225} a^{2} - \frac{1225752719447}{225} a - \frac{50545458893}{45} \) |
\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 11\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 32 a + 11\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a - 3\) , \( 84 a^{5} - 45 a^{4} - 565 a^{3} + 105 a^{2} + 891 a + 212\) , \( 298 a^{5} - 153 a^{4} - 1998 a^{3} + 365 a^{2} + 3103 a + 667\bigr] \) |
${y}^2+\left(-3a^{5}+a^{4}+20a^{3}-29a-11\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-3a^{2}-11a-3\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-20a^{3}+5a^{2}+32a+11\right){x}^{2}+\left(84a^{5}-45a^{4}-565a^{3}+105a^{2}+891a+212\right){x}+298a^{5}-153a^{4}-1998a^{3}+365a^{2}+3103a+667$ |
| 45.1-b4 |
45.1-b |
$4$ |
$4$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15398.21057$ |
1.72772 |
\( -\frac{252424}{15} a^{5} + \frac{27383}{5} a^{4} + \frac{338887}{3} a^{3} - \frac{171343}{15} a^{2} - \frac{2622451}{15} a - 36544 \) |
\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 11\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 32 a + 11\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a - 3\) , \( 19 a^{5} - 10 a^{4} - 135 a^{3} + 20 a^{2} + 231 a + 82\) , \( 21 a^{5} - 11 a^{4} - 150 a^{3} + 20 a^{2} + 261 a + 96\bigr] \) |
${y}^2+\left(-3a^{5}+a^{4}+20a^{3}-29a-11\right){x}{y}+\left(-a^{5}+a^{4}+7a^{3}-3a^{2}-11a-3\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-20a^{3}+5a^{2}+32a+11\right){x}^{2}+\left(19a^{5}-10a^{4}-135a^{3}+20a^{2}+231a+82\right){x}+21a^{5}-11a^{4}-150a^{3}+20a^{2}+261a+96$ |
| 45.1-c1 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5^{10} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2808.012961$ |
1.26026 |
\( \frac{814644996872}{253125} a^{5} + \frac{4632448800494}{759375} a^{4} - \frac{621554925707}{50625} a^{3} - \frac{23839748166988}{759375} a^{2} - \frac{13700111730136}{759375} a - \frac{392459283122}{151875} \) |
\( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 6\) , \( -a^{5} + 8 a^{3} + a^{2} - 14 a - 3\) , \( a^{2} - 2\) , \( -28 a^{5} + 35 a^{4} + 155 a^{3} - 141 a^{2} - 139 a - 17\) , \( 120 a^{5} - 152 a^{4} - 644 a^{3} + 565 a^{2} + 598 a + 102\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-6\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+8a^{3}+a^{2}-14a-3\right){x}^{2}+\left(-28a^{5}+35a^{4}+155a^{3}-141a^{2}-139a-17\right){x}+120a^{5}-152a^{4}-644a^{3}+565a^{2}+598a+102$ |
| 45.1-c2 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$2808.012961$ |
1.26026 |
\( \frac{238856356}{5} a^{5} - \frac{936662147}{15} a^{4} - \frac{1274072207}{5} a^{3} + \frac{3613285261}{15} a^{2} + \frac{3305121649}{15} a + \frac{493348744}{15} \) |
\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 3 a^{2} - 54 a - 15\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 16\) , \( -21 a^{5} + 14 a^{4} + 133 a^{3} - 39 a^{2} - 183 a - 52\) , \( -32 a^{5} + 32 a^{4} + 187 a^{3} - 112 a^{2} - 214 a - 51\bigr] \) |
${y}^2+\left(-3a^{5}+a^{4}+20a^{3}-30a-12\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-41a-16\right){y}={x}^{3}+\left(-5a^{5}+2a^{4}+34a^{3}-3a^{2}-54a-15\right){x}^{2}+\left(-21a^{5}+14a^{4}+133a^{3}-39a^{2}-183a-52\right){x}-32a^{5}+32a^{4}+187a^{3}-112a^{2}-214a-51$ |
| 45.1-c3 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{20} \cdot 5^{5} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$4$ |
\( 2 \) |
$1$ |
$702.0032403$ |
1.26026 |
\( -\frac{2235207536722976741518}{7381125} a^{5} - \frac{3847491343375465224361}{7381125} a^{4} + \frac{9023716509726943142789}{7381125} a^{3} + \frac{20003053994412435317929}{7381125} a^{2} + \frac{1968846152941296134387}{1476225} a + \frac{1298548105637621590364}{7381125} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 5\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 7 a\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 18\) , \( -323 a^{5} + 73 a^{4} + 2251 a^{3} + 142 a^{2} - 3617 a - 1489\) , \( 1252 a^{5} - 284 a^{4} - 8725 a^{3} - 565 a^{2} + 14006 a + 5768\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-11a-5\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-18\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+7a\right){x}^{2}+\left(-323a^{5}+73a^{4}+2251a^{3}+142a^{2}-3617a-1489\right){x}+1252a^{5}-284a^{4}-8725a^{3}-565a^{2}+14006a+5768$ |
| 45.1-c4 |
45.1-c |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{4} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$4$ |
\( 2 \) |
$1$ |
$702.0032403$ |
1.26026 |
\( \frac{767568164592729452}{45} a^{5} - \frac{967390709265225421}{45} a^{4} - \frac{4153706685300081856}{45} a^{3} + \frac{3699858317480481439}{45} a^{2} + \frac{756002343032818679}{9} a + \frac{609127105405722869}{45} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 10\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 3 a^{2} + 19 a + 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - a^{2} - 19 a - 8\) , \( 57 a^{5} - 41 a^{4} - 371 a^{3} + 103 a^{2} + 567 a + 110\) , \( 245 a^{5} - 68 a^{4} - 1745 a^{3} + 200 a^{2} + 2697 a + 559\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-10\right){x}{y}+\left(-2a^{5}+a^{4}+13a^{3}-a^{2}-19a-8\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+3a^{2}+19a+3\right){x}^{2}+\left(57a^{5}-41a^{4}-371a^{3}+103a^{2}+567a+110\right){x}+245a^{5}-68a^{4}-1745a^{3}+200a^{2}+2697a+559$ |
| 45.1-d1 |
45.1-d |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{2} \cdot 5^{7} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$366.7702968$ |
2.30454 |
\( \frac{1430847723840187894}{1875} a^{5} + \frac{2462936573108897663}{1875} a^{4} - \frac{5776449694269738587}{1875} a^{3} - \frac{4268257510246979394}{625} a^{2} - \frac{420112969221906737}{125} a - \frac{831253726470188812}{1875} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( 3 a^{5} - a^{4} - 20 a^{3} + a^{2} + 29 a + 10\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 13\) , \( 16 a^{5} + 14 a^{4} - 78 a^{3} - 81 a^{2} + 6 a + 9\) , \( 55 a^{5} + 96 a^{4} - 224 a^{3} - 498 a^{2} - 233 a - 29\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-30a-9\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-13\right){y}={x}^{3}+\left(3a^{5}-a^{4}-20a^{3}+a^{2}+29a+10\right){x}^{2}+\left(16a^{5}+14a^{4}-78a^{3}-81a^{2}+6a+9\right){x}+55a^{5}+96a^{4}-224a^{3}-498a^{2}-233a-29$ |
| 45.1-e1 |
45.1-e |
$2$ |
$2$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.010474223$ |
$41270.82159$ |
3.49220 |
\( -\frac{299322544022491}{3645} a^{5} + \frac{608425277207003}{3645} a^{4} + \frac{859340771116493}{3645} a^{3} - \frac{1149925182216842}{3645} a^{2} - \frac{191412328870237}{729} a - \frac{146365116009022}{3645} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - 2 a^{2} - 23 a - 6\) , \( -a^{4} + 5 a^{2} + 2 a - 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( 43 a^{5} - 27 a^{4} - 294 a^{3} + 95 a^{2} + 461 a + 29\) , \( 159 a^{5} - 52 a^{4} - 1092 a^{3} + 30 a^{2} + 1716 a + 593\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-2a^{2}-23a-6\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-3\right){x}^{2}+\left(43a^{5}-27a^{4}-294a^{3}+95a^{2}+461a+29\right){x}+159a^{5}-52a^{4}-1092a^{3}+30a^{2}+1716a+593$ |
| 45.1-e2 |
45.1-e |
$2$ |
$2$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.005237111$ |
$82541.64319$ |
3.49220 |
\( -\frac{337865}{9} a^{5} - \frac{8115143}{135} a^{4} + \frac{20010566}{45} a^{3} + \frac{2653301}{27} a^{2} - \frac{101043776}{135} a - \frac{23638802}{135} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - 2 a^{2} - 23 a - 6\) , \( -a^{4} + 5 a^{2} + 2 a - 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( 43 a^{5} - 22 a^{4} - 294 a^{3} + 60 a^{2} + 461 a + 89\) , \( -176 a^{5} + 79 a^{4} + 1193 a^{3} - 187 a^{2} - 1836 a - 391\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-2a^{2}-23a-6\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-3\right){x}^{2}+\left(43a^{5}-22a^{4}-294a^{3}+60a^{2}+461a+89\right){x}-176a^{5}+79a^{4}+1193a^{3}-187a^{2}-1836a-391$ |
| 45.1-f1 |
45.1-f |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{22} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1760.208474$ |
1.58000 |
\( \frac{2346897650445979}{885735} a^{5} - \frac{517584588238192}{885735} a^{4} - \frac{16313159822844242}{885735} a^{3} - \frac{121861357745033}{98415} a^{2} + \frac{1736751670938514}{59049} a + \frac{10685440990578398}{885735} \) |
\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -2 a^{5} + 15 a^{3} + 3 a^{2} - 26 a - 9\) , \( -a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( -8 a^{5} + 16 a^{4} + 55 a^{3} - 63 a^{2} - 100 a - 27\) , \( -40 a^{5} + 107 a^{4} + 230 a^{3} - 457 a^{2} - 316 a - 32\bigr] \) |
${y}^2+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){x}{y}+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){y}={x}^{3}+\left(-2a^{5}+15a^{3}+3a^{2}-26a-9\right){x}^{2}+\left(-8a^{5}+16a^{4}+55a^{3}-63a^{2}-100a-27\right){x}-40a^{5}+107a^{4}+230a^{3}-457a^{2}-316a-32$ |
| 45.1-g1 |
45.1-g |
$1$ |
$1$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{2} \cdot 5 \) |
$136.71433$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.004331393$ |
$144659.9245$ |
3.37458 |
\( \frac{647478001}{15} a^{5} - \frac{1315214113}{15} a^{4} - \frac{1860808178}{15} a^{3} + \frac{828316234}{5} a^{2} + 138294772 a + \frac{318834737}{15} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 9\) , \( 4 a^{5} - 2 a^{4} - 27 a^{3} + 4 a^{2} + 41 a + 13\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( 3 a^{5} + a^{4} - 24 a^{3} - 11 a^{2} + 45 a + 23\) , \( 6 a^{5} - 4 a^{4} - 45 a^{3} + 9 a^{2} + 84 a + 32\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-9\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-29a-12\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-27a^{3}+4a^{2}+41a+13\right){x}^{2}+\left(3a^{5}+a^{4}-24a^{3}-11a^{2}+45a+23\right){x}+6a^{5}-4a^{4}-45a^{3}+9a^{2}+84a+32$ |
| 55.1-a1 |
55.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11^{5} \) |
$139.01976$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7673.183934$ |
1.72190 |
\( \frac{8628781112}{805255} a^{5} - \frac{4495826021}{805255} a^{4} - \frac{56095018191}{805255} a^{3} + \frac{9664650959}{805255} a^{2} + \frac{15850063226}{161051} a + \frac{29361649564}{805255} \) |
\( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 6\) , \( a^{2} + a - 3\) , \( 16 a^{5} + 35 a^{4} - 56 a^{3} - 177 a^{2} - 119 a - 19\) , \( 280 a^{5} + 481 a^{4} - 1132 a^{3} - 2501 a^{2} - 1226 a - 164\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-5\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-6\right){x}^{2}+\left(16a^{5}+35a^{4}-56a^{3}-177a^{2}-119a-19\right){x}+280a^{5}+481a^{4}-1132a^{3}-2501a^{2}-1226a-164$ |
| 55.1-a2 |
55.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{2} \cdot 11^{10} \) |
$139.01976$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1918.295983$ |
1.72190 |
\( \frac{9355640786812955992}{129687123005} a^{5} - \frac{11834195442979152007}{129687123005} a^{4} - \frac{10127082634568257859}{25937424601} a^{3} + \frac{45295721042174947084}{129687123005} a^{2} + \frac{46151356036353912568}{129687123005} a + \frac{1486332274864254454}{25937424601} \) |
\( \bigl[a\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 13\) , \( 14 a^{5} - 5 a^{4} - 93 a^{3} + 12 a^{2} + 133 a + 20\) , \( 39 a^{5} - 13 a^{4} - 262 a^{3} + 21 a^{2} + 389 a + 87\bigr] \) |
${y}^2+a{x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-13\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){x}^{2}+\left(14a^{5}-5a^{4}-93a^{3}+12a^{2}+133a+20\right){x}+39a^{5}-13a^{4}-262a^{3}+21a^{2}+389a+87$ |
| 55.1-a3 |
55.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{5} \cdot 11 \) |
$139.01976$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7673.183934$ |
1.72190 |
\( -\frac{655063557448}{1375} a^{5} + \frac{2267781199879}{1375} a^{4} - \frac{287280939796}{1375} a^{3} - \frac{4531295286406}{1375} a^{2} + \frac{372336110472}{275} a + \frac{1676698717279}{1375} \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 41 a - 13\) , \( 5 a^{5} - 2 a^{4} - 34 a^{3} + 3 a^{2} + 54 a + 16\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( 283 a^{5} - 131 a^{4} - 1928 a^{3} + 312 a^{2} + 2985 a + 635\) , \( -3129 a^{5} + 1424 a^{4} + 21201 a^{3} - 3485 a^{2} - 32675 a - 6745\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-41a-13\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-29a-12\right){y}={x}^{3}+\left(5a^{5}-2a^{4}-34a^{3}+3a^{2}+54a+16\right){x}^{2}+\left(283a^{5}-131a^{4}-1928a^{3}+312a^{2}+2985a+635\right){x}-3129a^{5}+1424a^{4}+21201a^{3}-3485a^{2}-32675a-6745$ |
| 55.1-a4 |
55.1-a |
$4$ |
$10$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{10} \cdot 11^{2} \) |
$139.01976$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1918.295983$ |
1.72190 |
\( \frac{102828399466597382589532}{378125} a^{5} - \frac{22499976949168813685422}{378125} a^{4} - \frac{28595022222037473466624}{15125} a^{3} - \frac{49234219126300181077301}{378125} a^{2} + \frac{1141885379035918471784908}{378125} a + \frac{93988360608908048270083}{75625} \) |
\( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 18\) , \( 4 a^{5} - 2 a^{4} - 27 a^{3} + 4 a^{2} + 42 a + 12\) , \( a^{2} - 3\) , \( 674 a^{5} - 362 a^{4} - 4462 a^{3} + 826 a^{2} + 6879 a + 1462\) , \( -8109 a^{5} + 3024 a^{4} + 56722 a^{3} - 7916 a^{2} - 88065 a - 18257\bigr] \) |
${y}^2+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-18\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-27a^{3}+4a^{2}+42a+12\right){x}^{2}+\left(674a^{5}-362a^{4}-4462a^{3}+826a^{2}+6879a+1462\right){x}-8109a^{5}+3024a^{4}+56722a^{3}-7916a^{2}-88065a-18257$ |
| 55.1-b1 |
55.1-b |
$2$ |
$3$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11 \) |
$139.01976$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.103910364$ |
$7478.931726$ |
4.18545 |
\( -\frac{8946008034}{55} a^{5} + \frac{7854817887}{55} a^{4} + \frac{59752282247}{55} a^{3} - \frac{47789949173}{55} a^{2} - \frac{10299559591}{11} a - \frac{8273165333}{55} \) |
\( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( 4 a^{5} - a^{4} - 27 a^{3} - a^{2} + 42 a + 16\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 31 a - 10\) , \( 9 a^{5} - 10 a^{4} - 43 a^{3} + 8 a^{2} + 72 a + 26\) , \( -37 a^{5} + 75 a^{4} + 112 a^{3} - 157 a^{2} - 114 a - 13\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+13a^{3}-2a^{2}-19a-5\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-31a-10\right){y}={x}^{3}+\left(4a^{5}-a^{4}-27a^{3}-a^{2}+42a+16\right){x}^{2}+\left(9a^{5}-10a^{4}-43a^{3}+8a^{2}+72a+26\right){x}-37a^{5}+75a^{4}+112a^{3}-157a^{2}-114a-13$ |
| 55.1-b2 |
55.1-b |
$2$ |
$3$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{3} \) |
$139.01976$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.034636788$ |
$7478.931726$ |
4.18545 |
\( \frac{35211521}{33275} a^{5} + \frac{3563927}{33275} a^{4} - \frac{247874618}{33275} a^{3} - \frac{87096888}{33275} a^{2} + \frac{16267222}{1331} a + \frac{238040557}{33275} \) |
\( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 19\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 7 a + 4\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 31 a - 10\) , \( 40 a^{5} - 9 a^{4} - 279 a^{3} - 20 a^{2} + 451 a + 188\) , \( 92 a^{5} - 18 a^{4} - 641 a^{3} - 53 a^{2} + 1023 a + 424\bigr] \) |
${y}^2+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-19\right){x}{y}+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-31a-10\right){y}={x}^{3}+\left(a^{5}-6a^{3}-2a^{2}+7a+4\right){x}^{2}+\left(40a^{5}-9a^{4}-279a^{3}-20a^{2}+451a+188\right){x}+92a^{5}-18a^{4}-641a^{3}-53a^{2}+1023a+424$ |
| 55.1-c1 |
55.1-c |
$4$ |
$15$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( - 5 \cdot 11 \) |
$139.01976$ |
$(-2a^5+a^4+13a^3-2a^2-19a-5), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$10216.72289$ |
1.01897 |
\( -\frac{140524896}{55} a^{5} - \frac{317747392}{55} a^{4} + \frac{268980858}{55} a^{3} + \frac{896813163}{55} a^{2} + \frac{94639614}{11} a + \frac{65297843}{55} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{5} - 7 a^{3} - a^{2} + 11 a + 4\) , \( 3 a^{5} - 2 a^{4} - 23 a^{3} + 5 a^{2} + 38 a + 10\) , \( 3 a^{5} - 19 a^{3} + 27 a + 5\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{5}-7a^{3}-a^{2}+11a+4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(3a^{5}-2a^{4}-23a^{3}+5a^{2}+38a+10\right){x}+3a^{5}-19a^{3}+27a+5$ |
*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.
