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 |
3.1-a1 |
3.1-a |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$38.52033$ |
$(-a^4+a^3+4a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$644.5665158$ |
1.66889284 |
\( \frac{48552525146}{3} a^{4} + \frac{36513739424}{3} a^{3} - \frac{263855133073}{3} a^{2} - \frac{344088812371}{3} a - \frac{64560563147}{3} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - 2 a + 4\) , \( a^{3} - 3 a - 1\) , \( a^{4} - 5 a^{2} - 2 a + 1\) , \( 18 a^{4} - 7 a^{3} - 97 a^{2} - 23 a + 65\) , \( 57 a^{4} - 13 a^{3} - 336 a^{2} - 93 a + 245\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-2a+4\right){x}{y}+\left(a^{4}-5a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(18a^{4}-7a^{3}-97a^{2}-23a+65\right){x}+57a^{4}-13a^{3}-336a^{2}-93a+245$ |
3.1-b1 |
3.1-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$38.52033$ |
$(-a^4+a^3+4a^2-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.246308436$ |
$257.4397019$ |
1.64178212 |
\( -\frac{2015468}{27} a^{4} + \frac{1234648}{9} a^{3} + \frac{5212205}{27} a^{2} - \frac{4186502}{27} a - \frac{1133291}{27} \) |
\( \bigl[a^{4} - 6 a^{2} - 2 a + 4\) , \( -a\) , \( 2 a^{4} - a^{3} - 10 a^{2} - 2 a + 5\) , \( -a\) , \( a^{3} - 2 a^{2} - 3 a + 2\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-2a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}-2a+5\right){y}={x}^{3}-a{x}^{2}-a{x}+a^{3}-2a^{2}-3a+2$ |
3.1-b2 |
3.1-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$38.52033$ |
$(-a^4+a^3+4a^2-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.082102812$ |
$6950.871953$ |
1.64178212 |
\( 51249 a^{4} - \frac{200146}{3} a^{3} - \frac{670325}{3} a^{2} + 141085 a + \frac{101900}{3} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 4\) , \( -a^{2} + a + 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} + 2 a + 19\) , \( 3 a^{4} - 2 a^{3} - 18 a^{2} + 2 a + 18\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+4\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(3a^{4}-2a^{3}-18a^{2}+2a+19\right){x}+3a^{4}-2a^{3}-18a^{2}+2a+18$ |
9.1-a1 |
9.1-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$42.99343$ |
$(-a^4+a^3+4a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$409.1922701$ |
2.11893741 |
\( -\frac{2015468}{27} a^{4} + \frac{1234648}{9} a^{3} + \frac{5212205}{27} a^{2} - \frac{4186502}{27} a - \frac{1133291}{27} \) |
\( \bigl[a^{4} - 6 a^{2} - 2 a + 5\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a\) , \( a^{4} - 6 a^{2} - 2 a + 5\) , \( -2 a^{4} + 6 a^{3} + a^{2} - 13 a + 6\) , \( 5 a^{3} - 10 a^{2} - 13 a + 13\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-2a+5\right){x}{y}+\left(a^{4}-6a^{2}-2a+5\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a\right){x}^{2}+\left(-2a^{4}+6a^{3}+a^{2}-13a+6\right){x}+5a^{3}-10a^{2}-13a+13$ |
9.1-a2 |
9.1-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$42.99343$ |
$(-a^4+a^3+4a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$409.1922701$ |
2.11893741 |
\( 51249 a^{4} - \frac{200146}{3} a^{3} - \frac{670325}{3} a^{2} + 141085 a + \frac{101900}{3} \) |
\( \bigl[a + 1\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 5 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( -2 a^{4} + a^{3} + 13 a^{2} - 2 a - 5\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 5 a - 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-5a-2\right){x}^{2}+\left(-2a^{4}+a^{3}+13a^{2}-2a-5\right){x}-3a^{4}+4a^{3}+13a^{2}-5a-6$ |
9.1-b1 |
9.1-b |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$42.99343$ |
$(-a^4+a^3+4a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$241.2942316$ |
1.24950399 |
\( \frac{48552525146}{3} a^{4} + \frac{36513739424}{3} a^{3} - \frac{263855133073}{3} a^{2} - \frac{344088812371}{3} a - \frac{64560563147}{3} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - a + 4\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 27 a^{4} + 23 a^{3} - 147 a^{2} - 204 a - 41\) , \( 175 a^{4} + 132 a^{3} - 950 a^{2} - 1241 a - 236\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-a+4\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(27a^{4}+23a^{3}-147a^{2}-204a-41\right){x}+175a^{4}+132a^{3}-950a^{2}-1241a-236$ |
11.1-a1 |
11.1-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$43.86490$ |
$(a^3-3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2990.139183$ |
2.58066042 |
\( -\frac{454863982}{1331} a^{4} + \frac{841373572}{1331} a^{3} + \frac{1180114367}{1331} a^{2} - \frac{845250080}{1331} a - \frac{243787469}{1331} \) |
\( \bigl[1\) , \( 2 a^{4} - a^{3} - 10 a^{2} - 2 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 8 a + 4\) , \( -7 a^{4} + 9 a^{3} + 31 a^{2} - 19 a - 7\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+3\right){y}={x}^{3}+\left(2a^{4}-a^{3}-10a^{2}-2a+3\right){x}^{2}+\left(2a^{4}-3a^{3}-9a^{2}+8a+4\right){x}-7a^{4}+9a^{3}+31a^{2}-19a-7$ |
11.1-a2 |
11.1-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$43.86490$ |
$(a^3-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$110.7458956$ |
2.58066042 |
\( -\frac{10166061508}{11} a^{4} - \frac{23978704058}{11} a^{3} - \frac{586048733}{11} a^{2} + \frac{17454979979}{11} a + \frac{655388650}{11} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 4\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 3\) , \( 1\) , \( 7 a^{4} + 3 a^{3} - 35 a^{2} - 42 a - 8\) , \( 44 a^{4} + 33 a^{3} - 239 a^{2} - 312 a - 59\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+4\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-3\right){x}^{2}+\left(7a^{4}+3a^{3}-35a^{2}-42a-8\right){x}+44a^{4}+33a^{3}-239a^{2}-312a-59$ |
11.1-b1 |
11.1-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{6} \) |
$43.86490$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.083190489$ |
$1181.601995$ |
2.54510441 |
\( -\frac{143120245443970}{1771561} a^{4} + \frac{32848717099832}{1771561} a^{3} + \frac{850953185668925}{1771561} a^{2} + \frac{234534070086843}{1771561} a - \frac{625846989869778}{1771561} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a - 1\) , \( 0\) , \( -17 a^{4} + 8 a^{3} + 94 a^{2} + 18 a - 63\) , \( 41 a^{4} - 262 a^{2} - 87 a + 200\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a-1\right){x}^{2}+\left(-17a^{4}+8a^{3}+94a^{2}+18a-63\right){x}+41a^{4}-262a^{2}-87a+200$ |
11.1-b2 |
11.1-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$43.86490$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.027730163$ |
$3544.805987$ |
2.54510441 |
\( -\frac{21630}{121} a^{4} + \frac{46081}{121} a^{3} + \frac{87231}{121} a^{2} - \frac{178722}{121} a - \frac{69418}{121} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( -4 a^{4} + 12 a^{3} + 15 a^{2} - 45 a - 13\) , \( -25 a^{4} + a^{3} + 126 a^{2} + 82 a + 11\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-7a-2\right){x}^{2}+\left(-4a^{4}+12a^{3}+15a^{2}-45a-13\right){x}-25a^{4}+a^{3}+126a^{2}+82a+11$ |
17.1-a1 |
17.1-a |
$2$ |
$2$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$45.81659$ |
$(a^4-a^3-4a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$0.081162104$ |
$11741.22145$ |
3.08416285 |
\( \frac{29310}{4913} a^{4} - \frac{1987561}{4913} a^{3} + \frac{7447808}{4913} a^{2} + \frac{907028}{4913} a - \frac{4056528}{4913} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( -a^{2} - a + 2\) , \( 2 a^{4} - a^{3} - 10 a^{2} - a + 4\) , \( -a^{4} + 2 a^{3} + 4 a^{2}\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 2 a + 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}-a+4\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-a^{4}+2a^{3}+4a^{2}\right){x}+a^{4}-2a^{3}-5a^{2}+2a+1$ |
17.1-a2 |
17.1-a |
$2$ |
$2$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{6} \) |
$45.81659$ |
$(a^4-a^3-4a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$0.162324208$ |
$2935.305363$ |
3.08416285 |
\( \frac{86301098263921}{24137569} a^{4} - \frac{134160130413778}{24137569} a^{3} - \frac{262091602038988}{24137569} a^{2} + \frac{122048621862715}{24137569} a + \frac{86921043725991}{24137569} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - 2 a + 4\) , \( -a^{3} + 5 a + 1\) , \( a^{4} - 6 a^{2} - 3 a + 4\) , \( 15 a^{4} + 36 a^{3} - 92 a^{2} - 226 a - 55\) , \( -128 a^{4} - 81 a^{3} + 689 a^{2} + 833 a + 149\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-2a+4\right){x}{y}+\left(a^{4}-6a^{2}-3a+4\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(15a^{4}+36a^{3}-92a^{2}-226a-55\right){x}-128a^{4}-81a^{3}+689a^{2}+833a+149$ |
17.1-b1 |
17.1-b |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$45.81659$ |
$(a^4-a^3-4a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$1$ |
$95.82754580$ |
0.744341668 |
\( \frac{7047993802}{4913} a^{4} + \frac{4469500853}{4913} a^{3} - \frac{40859802989}{4913} a^{2} - \frac{51998809797}{4913} a - \frac{9659255326}{4913} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - 6 a^{2} - 2 a + 5\) , \( 5 a^{4} - 3 a^{3} - 22 a^{2} + a + 3\) , \( 30 a^{4} - 36 a^{3} - 130 a^{2} + 72 a + 16\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{4}-6a^{2}-2a+5\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(5a^{4}-3a^{3}-22a^{2}+a+3\right){x}+30a^{4}-36a^{3}-130a^{2}+72a+16$ |
17.1-c1 |
17.1-c |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$45.81659$ |
$(a^4-a^3-4a^2+a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.265197683$ |
$5589.734783$ |
2.13230407 |
\( -\frac{1686251707}{17} a^{4} + \frac{3067395368}{17} a^{3} + \frac{4540008973}{17} a^{2} - \frac{3202236406}{17} a - \frac{927898646}{17} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - a + 4\) , \( a^{2} - a - 4\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{3} + 4 a^{2} + a - 5\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{3}+a^{2}+6a\right){x}+a^{3}+4a^{2}+a-5$ |
17.1-c2 |
17.1-c |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$45.81659$ |
$(a^4-a^3-4a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.795593051$ |
$207.0272141$ |
2.13230407 |
\( \frac{2776213341687}{4913} a^{4} - \frac{3483531945827}{4913} a^{3} - \frac{12286608223006}{4913} a^{2} + \frac{7088902291859}{4913} a + \frac{2211440063376}{4913} \) |
\( \bigl[a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -6 a^{4} + 7 a^{3} + 25 a^{2} - 6 a - 8\) , \( 8 a^{4} - 16 a^{3} - 19 a^{2} + 21 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+2a+2\right){x}^{2}+\left(-6a^{4}+7a^{3}+25a^{2}-6a-8\right){x}+8a^{4}-16a^{3}-19a^{2}+21a-2$ |
19.1-a1 |
19.1-a |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$46.32903$ |
$(a^4-6a^2-2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1.261066115$ |
$324.4698867$ |
5.29715851 |
\( -\frac{5104253882}{6859} a^{4} + \frac{1220593775}{6859} a^{3} + \frac{30252291291}{6859} a^{2} + \frac{8243716709}{6859} a - \frac{22196716214}{6859} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 5 a + 1\) , \( a\) , \( -2 a^{4} + 4 a^{3} + 4 a^{2} - 3 a - 1\) , \( -18 a^{4} + 33 a^{3} + 48 a^{2} - 34 a - 10\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){x}{y}+a{y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+5a+1\right){x}^{2}+\left(-2a^{4}+4a^{3}+4a^{2}-3a-1\right){x}-18a^{4}+33a^{3}+48a^{2}-34a-10$ |
19.1-b1 |
19.1-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$46.32903$ |
$(a^4-6a^2-2a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2678.955014$ |
0.770696918 |
\( -\frac{32482406302}{19} a^{4} + \frac{7811360669}{19} a^{3} + \frac{192623711086}{19} a^{2} + \frac{51706894603}{19} a - \frac{140761024172}{19} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( 2 a^{4} - 5 a^{3} - 6 a^{2} + 17 a - 3\) , \( -7 a^{4} + 9 a^{3} + 31 a^{2} - 19 a - 7\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{4}-5a^{3}-6a^{2}+17a-3\right){x}-7a^{4}+9a^{3}+31a^{2}-19a-7$ |
19.1-b2 |
19.1-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$46.32903$ |
$(a^4-6a^2-2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$99.22055609$ |
0.770696918 |
\( -\frac{2961870404945}{6859} a^{4} - \frac{7550121359867}{6859} a^{3} - \frac{1484343374431}{6859} a^{2} + \frac{5098089183739}{6859} a + \frac{1160747437682}{6859} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - 2 a + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a - 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( 39 a^{4} - 50 a^{3} - 171 a^{2} + 102 a + 28\) , \( -56 a^{4} + 70 a^{3} + 248 a^{2} - 143 a - 45\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-2a+5\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a-2\right){x}^{2}+\left(39a^{4}-50a^{3}-171a^{2}+102a+28\right){x}-56a^{4}+70a^{3}+248a^{2}-143a-45$ |
19.2-a1 |
19.2-a |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$46.32903$ |
$(-a^2+a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.027484876$ |
$10998.26196$ |
3.91334891 |
\( \frac{10324997}{19} a^{4} + \frac{69118}{19} a^{3} - \frac{52924154}{19} a^{2} - \frac{35704501}{19} a - \frac{2378951}{19} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - 2 a + 4\) , \( a^{4} - 6 a^{2} - 2 a + 4\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 5 a^{4} - 4 a^{3} - 23 a^{2} - 4 a + 15\) , \( 4 a^{4} - 2 a^{3} - 22 a^{2} - 3 a + 14\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-2a+4\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-6a^{2}-2a+4\right){x}^{2}+\left(5a^{4}-4a^{3}-23a^{2}-4a+15\right){x}+4a^{4}-2a^{3}-22a^{2}-3a+14$ |
19.2-b1 |
19.2-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$46.32903$ |
$(-a^2+a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$224.7795905$ |
1.74597830 |
\( \frac{7047944989}{361} a^{4} + \frac{5330059098}{361} a^{3} - \frac{38202683587}{361} a^{2} - \frac{49857243602}{361} a - \frac{9354544836}{361} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + a\) , \( -3 a^{4} + a^{3} + 22 a^{2} + 8 a - 22\) , \( 8 a^{4} - 45 a^{2} - 14 a + 31\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}^{2}+\left(-3a^{4}+a^{3}+22a^{2}+8a-22\right){x}+8a^{4}-45a^{2}-14a+31$ |
19.2-b2 |
19.2-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$46.32903$ |
$(-a^2+a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$6069.048946$ |
1.74597830 |
\( \frac{51927642817}{19} a^{4} - \frac{11869240569}{19} a^{3} - \frac{308852867158}{19} a^{2} - \frac{85187586863}{19} a + \frac{227182129482}{19} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 4\) , \( -a^{2} + a + 4\) , \( 2 a^{4} - a^{3} - 10 a^{2} - 2 a + 5\) , \( 2 a^{4} - a^{3} - 12 a^{2} - a + 13\) , \( 3 a^{4} - a^{3} - 18 a^{2} - 4 a + 15\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}-2a+5\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(2a^{4}-a^{3}-12a^{2}-a+13\right){x}+3a^{4}-a^{3}-18a^{2}-4a+15$ |
19.2-c1 |
19.2-c |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$46.32903$ |
$(-a^2+a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$4659.856324$ |
1.34057380 |
\( \frac{118279}{19} a^{4} - \frac{117089}{19} a^{3} - \frac{575423}{19} a^{2} + \frac{200859}{19} a + \frac{204172}{19} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} - a + 3\) , \( a^{4} - 6 a^{2} - 3 a + 5\) , \( -27 a^{4} - 19 a^{3} + 147 a^{2} + 186 a + 35\) , \( 117 a^{4} + 90 a^{3} - 636 a^{2} - 840 a - 163\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{4}-6a^{2}-3a+5\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-27a^{4}-19a^{3}+147a^{2}+186a+35\right){x}+117a^{4}+90a^{3}-636a^{2}-840a-163$ |
19.2-c2 |
19.2-c |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$46.32903$ |
$(-a^2+a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$19.17636347$ |
1.34057380 |
\( \frac{15448858568678}{361} a^{4} + \frac{657176984179}{361} a^{3} - \frac{100455928280384}{361} a^{2} - \frac{34661078892237}{361} a + \frac{77660697257826}{361} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{3} - 3 a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 2 a + 3\) , \( 59 a^{4} + 63 a^{3} - 319 a^{2} - 502 a - 125\) , \( 603 a^{4} + 495 a^{3} - 3278 a^{2} - 4466 a - 902\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+2a+3\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(59a^{4}+63a^{3}-319a^{2}-502a-125\right){x}+603a^{4}+495a^{3}-3278a^{2}-4466a-902$ |
19.2-d1 |
19.2-d |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$46.32903$ |
$(-a^2+a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$417.4536678$ |
1.08085887 |
\( \frac{73755104967}{19} a^{4} + \frac{183880904530}{19} a^{3} + \frac{23172544843}{19} a^{2} - \frac{139505226971}{19} a - \frac{31103091018}{19} \) |
\( \bigl[a^{4} - 5 a^{2} - 3 a + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -6 a^{4} + 6 a^{3} + 27 a^{2} - 2 a - 16\) , \( 2 a^{4} - 9 a^{3} + 4 a^{2} + 14 a - 11\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-a-2\right){x}^{2}+\left(-6a^{4}+6a^{3}+27a^{2}-2a-16\right){x}+2a^{4}-9a^{3}+4a^{2}+14a-11$ |
21.1-a1 |
21.1-a |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{2} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.107088239$ |
$476.5501789$ |
2.64265897 |
\( -\frac{23304651808}{1323} a^{4} + \frac{15980017082}{3969} a^{3} + \frac{415833114493}{3969} a^{2} + \frac{38231594393}{1323} a - \frac{305880081721}{3969} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( a^{3} - 4 a - 2\) , \( 1\) , \( -3 a^{4} + a^{3} + 17 a^{2} + 6 a - 8\) , \( -3 a^{4} + 3 a^{3} + 14 a^{2} - a - 10\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+a+3\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(-3a^{4}+a^{3}+17a^{2}+6a-8\right){x}-3a^{4}+3a^{3}+14a^{2}-a-10$ |
21.1-b1 |
21.1-b |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{4} \cdot 7^{2} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$86.79484738$ |
1.79781352 |
\( \frac{4981099478753521762}{441} a^{4} + \frac{416224075893099975}{49} a^{3} - \frac{27069419449656648184}{441} a^{2} - \frac{35300751101598793331}{441} a - \frac{6623396026616367485}{441} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 7 a + 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 2 a + 4\) , \( -3 a^{4} + 5 a^{3} + 16 a^{2} - 15 a - 7\) , \( -68 a^{4} + 128 a^{3} + 180 a^{2} - 139 a - 48\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+2a+4\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+7a+2\right){x}^{2}+\left(-3a^{4}+5a^{3}+16a^{2}-15a-7\right){x}-68a^{4}+128a^{3}+180a^{2}-139a-48$ |
21.1-c1 |
21.1-c |
$4$ |
$6$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{4} \cdot 7^{2} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$6418.888756$ |
1.84662219 |
\( -\frac{2288585756183567}{441} a^{4} + \frac{2871372062141201}{441} a^{3} + \frac{1125445504664924}{49} a^{2} - \frac{5842518547141229}{441} a - \frac{202677679717652}{49} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 3\) , \( a^{4} - 5 a^{2} - 3 a + 1\) , \( -142 a^{4} - 98 a^{3} + 769 a^{2} + 962 a + 169\) , \( -5765 a^{4} - 4332 a^{3} + 31326 a^{2} + 40840 a + 7669\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a\right){x}{y}+\left(a^{4}-5a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-6a-3\right){x}^{2}+\left(-142a^{4}-98a^{3}+769a^{2}+962a+169\right){x}-5765a^{4}-4332a^{3}+31326a^{2}+40840a+7669$ |
21.1-c2 |
21.1-c |
$4$ |
$6$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7 \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$12837.77751$ |
1.84662219 |
\( -\frac{7594858}{7} a^{4} + \frac{28519802}{21} a^{3} + \frac{100825498}{21} a^{2} - \frac{19316013}{7} a - \frac{18074929}{21} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - 2 a + 4\) , \( a^{3} - a^{2} - 5 a\) , \( a^{4} - 6 a^{2} - 3 a + 4\) , \( -2 a^{4} - a^{3} + 4 a^{2} - 2 a - 1\) , \( 4 a^{4} + 11 a^{3} + 3 a^{2} - 8 a - 2\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-2a+4\right){x}{y}+\left(a^{4}-6a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-2a^{4}-a^{3}+4a^{2}-2a-1\right){x}+4a^{4}+11a^{3}+3a^{2}-8a-2$ |
21.1-c3 |
21.1-c |
$4$ |
$6$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7^{3} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$475.4732412$ |
1.84662219 |
\( -\frac{462018887}{9261} a^{4} - \frac{99420803}{3087} a^{3} + \frac{2491580312}{9261} a^{2} + \frac{3055709116}{9261} a + \frac{495730195}{9261} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - a - 4\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( -7 a^{4} - a^{3} + 52 a^{2} + 25 a - 43\) , \( -18 a^{4} + 4 a^{3} + 114 a^{2} + 41 a - 92\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-a-4\right){x}^{2}+\left(-7a^{4}-a^{3}+52a^{2}+25a-43\right){x}-18a^{4}+4a^{3}+114a^{2}+41a-92$ |
21.1-c4 |
21.1-c |
$4$ |
$6$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{12} \cdot 7^{6} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$237.7366206$ |
1.84662219 |
\( \frac{2087020500617723}{85766121} a^{4} - \frac{559677071477894}{28588707} a^{3} - \frac{9952117357522511}{85766121} a^{2} - \frac{750379776589669}{85766121} a + \frac{6239531840717912}{85766121} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -2 a^{4} + a^{3} + 10 a^{2} + 2 a - 3\) , \( a^{4} - 6 a^{2} - 2 a + 5\) , \( 27 a^{4} - 35 a^{3} - 127 a^{2} + 88 a + 21\) , \( -129 a^{4} + 167 a^{3} + 552 a^{2} - 310 a - 104\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{4}-6a^{2}-2a+5\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+10a^{2}+2a-3\right){x}^{2}+\left(27a^{4}-35a^{3}-127a^{2}+88a+21\right){x}-129a^{4}+167a^{3}+552a^{2}-310a-104$ |
21.1-d1 |
21.1-d |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7 \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.015876429$ |
$12592.00913$ |
2.58808521 |
\( -\frac{232219}{21} a^{4} + \frac{60413}{21} a^{3} + \frac{1384583}{21} a^{2} + \frac{344615}{21} a - \frac{1016363}{21} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 2\) , \( -a^{3} + a^{2} + 4 a - 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-3a-2\right){x}-a^{3}+a^{2}+4a-1$ |
21.1-e1 |
21.1-e |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{3} \cdot 7 \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3454.081665$ |
0.993689734 |
\( -\frac{475591617142960}{63} a^{4} + \frac{108746547323297}{63} a^{3} + \frac{2828621799299357}{63} a^{2} + \frac{780123263192960}{63} a - \frac{2080606889405234}{63} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 4\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 5 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + a + 3\) , \( 40 a^{4} - 54 a^{3} - 182 a^{2} + 107 a + 34\) , \( -496 a^{4} + 634 a^{3} + 2209 a^{2} - 1281 a - 398\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+5a+1\right){x}^{2}+\left(40a^{4}-54a^{3}-182a^{2}+107a+34\right){x}-496a^{4}+634a^{3}+2209a^{2}-1281a-398$ |
21.1-e2 |
21.1-e |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{9} \cdot 7^{3} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$127.9289505$ |
0.993689734 |
\( \frac{473573304141656066}{83349} a^{4} + \frac{356148999087585962}{83349} a^{3} - \frac{2573599294264710613}{83349} a^{2} - \frac{3356185346349688297}{83349} a - \frac{629713083067475984}{83349} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 5 a + 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -6 a^{4} + 2 a^{3} + 23 a^{2} - 16 a - 14\) , \( 9 a^{4} - 36 a^{3} - 85 a^{2} + 24 a + 19\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+5a+2\right){x}^{2}+\left(-6a^{4}+2a^{3}+23a^{2}-16a-14\right){x}+9a^{4}-36a^{3}-85a^{2}+24a+19$ |
21.1-f1 |
21.1-f |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{13} \cdot 7^{11} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$1$ |
$53.61079825$ |
1.80449772 |
\( \frac{49524634691895007}{4324413586941} a^{4} + \frac{205304443762023169}{4324413586941} a^{3} - \frac{456347051666165006}{4324413586941} a^{2} - \frac{934003345294475972}{4324413586941} a - \frac{179969886370778254}{4324413586941} \) |
\( \bigl[a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 4 a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 2 a + 3\) , \( -30 a^{4} + 60 a^{3} + 75 a^{2} - 74 a - 15\) , \( -201 a^{4} + 359 a^{3} + 547 a^{2} - 358 a - 106\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+2a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-4a-1\right){x}^{2}+\left(-30a^{4}+60a^{3}+75a^{2}-74a-15\right){x}-201a^{4}+359a^{3}+547a^{2}-358a-106$ |
21.1-g1 |
21.1-g |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{4} \cdot 7^{2} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.005058621$ |
$8214.240442$ |
4.30348541 |
\( -\frac{31063030867}{147} a^{4} - \frac{237604424104}{441} a^{3} - \frac{46686073772}{441} a^{2} + \frac{53510055128}{147} a + \frac{36547770272}{441} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 6 a - 1\) , \( -2 a^{4} + 2 a^{3} + 8 a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a+1\right){x}^{2}+\left(-a^{4}+a^{3}+5a^{2}-6a-1\right){x}-2a^{4}+2a^{3}+8a^{2}-3a-1$ |
21.1-h1 |
21.1-h |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{3} \cdot 7^{3} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$185.1575880$ |
1.43821389 |
\( -\frac{28992974277311}{3087} a^{4} - \frac{73923497501477}{3087} a^{3} - \frac{14525116565567}{3087} a^{2} + \frac{49944265699303}{3087} a + \frac{11371126127498}{3087} \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - a + 4\) , \( a^{3} - 4 a - 1\) , \( a^{4} - 5 a^{2} - 3 a + 1\) , \( 6 a^{4} + 8 a^{3} - 33 a^{2} - 54 a - 7\) , \( 232 a^{4} + 177 a^{3} - 1260 a^{2} - 1650 a - 307\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-a+4\right){x}{y}+\left(a^{4}-5a^{2}-3a+1\right){y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(6a^{4}+8a^{3}-33a^{2}-54a-7\right){x}+232a^{4}+177a^{3}-1260a^{2}-1650a-307$ |
21.1-h2 |
21.1-h |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3 \cdot 7 \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$4999.254876$ |
1.43821389 |
\( \frac{1121960141170}{21} a^{4} - \frac{1407658654055}{21} a^{3} - \frac{4965652799930}{21} a^{2} + \frac{2864237618377}{21} a + \frac{894246985616}{21} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( 42 a^{4} - 53 a^{3} - 186 a^{2} + 107 a + 34\) , \( -182 a^{4} + 228 a^{3} + 805 a^{2} - 464 a - 145\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-1\right){x}^{2}+\left(42a^{4}-53a^{3}-186a^{2}+107a+34\right){x}-182a^{4}+228a^{3}+805a^{2}-464a-145$ |
21.1-i1 |
21.1-i |
$4$ |
$4$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7 \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5277.020076$ |
1.70788833 |
\( -\frac{3294785}{21} a^{4} + \frac{273501}{7} a^{3} + \frac{19486322}{21} a^{2} + \frac{5135038}{21} a - \frac{14138480}{21} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 5\) , \( a^{4} - a^{3} - 4 a^{2} - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 4 a + 5\) , \( 5 a^{4} - 6 a^{3} - 21 a^{2} + 6 a + 7\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+5\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}-1\right){x}^{2}+\left(-a^{4}+2a^{3}+2a^{2}-4a+5\right){x}+5a^{4}-6a^{3}-21a^{2}+6a+7$ |
21.1-i2 |
21.1-i |
$4$ |
$4$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7 \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$329.8137547$ |
1.70788833 |
\( -\frac{16698471987145}{567} a^{4} - \frac{3143037698993}{189} a^{3} + \frac{184031373949495}{567} a^{2} + \frac{250716717232862}{567} a + \frac{47625562764284}{567} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 4\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} - a + 4\) , \( -636 a^{4} + 1125 a^{3} + 1790 a^{2} - 1178 a - 402\) , \( 17912 a^{4} - 32563 a^{3} - 48335 a^{2} + 34214 a + 9725\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+4\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}-a+4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-636a^{4}+1125a^{3}+1790a^{2}-1178a-402\right){x}+17912a^{4}-32563a^{3}-48335a^{2}+34214a+9725$ |
21.1-i3 |
21.1-i |
$4$ |
$4$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1319.255019$ |
1.70788833 |
\( \frac{46191820920929}{441} a^{4} - \frac{3519410860012}{147} a^{3} - \frac{274737532785155}{441} a^{2} - \frac{75777677613901}{441} a + \frac{202088172228023}{441} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 5\) , \( a^{4} - a^{3} - 4 a^{2} - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( -21 a^{4} + 32 a^{3} + 67 a^{2} - 29 a - 20\) , \( 56 a^{4} - 119 a^{3} - 113 a^{2} + 150 a - 17\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+5\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}-1\right){x}^{2}+\left(-21a^{4}+32a^{3}+67a^{2}-29a-20\right){x}+56a^{4}-119a^{3}-113a^{2}+150a-17$ |
21.1-i4 |
21.1-i |
$4$ |
$4$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{4} \) |
$46.79503$ |
$(-a^4+a^3+4a^2-1), (a^4-a^3-5a^2+a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$41.22671934$ |
1.70788833 |
\( \frac{351241440255450052050855389}{7203} a^{4} - \frac{26761406563491791450919195}{2401} a^{3} - \frac{2089097857164486824454988835}{7203} a^{2} - \frac{576213491755072751413010806}{7203} a + \frac{1536672459773051588137309508}{7203} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 5\) , \( a^{4} - a^{3} - 4 a^{2} - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( -86 a^{4} + 57 a^{3} + 432 a^{2} + 56 a - 280\) , \( -540 a^{4} + 148 a^{3} + 3163 a^{2} + 836 a - 2309\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+5\right){x}{y}+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}-1\right){x}^{2}+\left(-86a^{4}+57a^{3}+432a^{2}+56a-280\right){x}-540a^{4}+148a^{3}+3163a^{2}+836a-2309$ |
27.2-a1 |
27.2-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$47.98596$ |
$(-a^4+a^3+4a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$692.0512954$ |
1.79183905 |
\( -94651371965 a^{4} + 115679364825 a^{3} + 428362635873 a^{2} - 245209014322 a - 76788326175 \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( -2 a^{4} + a^{3} + 10 a^{2} + a - 4\) , \( a^{4} - 6 a^{2} - 3 a + 5\) , \( -14 a^{4} + 16 a^{3} + 61 a^{2} - 30 a - 12\) , \( -18 a^{4} + 15 a^{3} + 75 a^{2} - 30 a - 19\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+3\right){x}{y}+\left(a^{4}-6a^{2}-3a+5\right){y}={x}^{3}+\left(-2a^{4}+a^{3}+10a^{2}+a-4\right){x}^{2}+\left(-14a^{4}+16a^{3}+61a^{2}-30a-12\right){x}-18a^{4}+15a^{3}+75a^{2}-30a-19$ |
27.2-a2 |
27.2-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{5} \) |
$47.98596$ |
$(-a^4+a^3+4a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$692.0512954$ |
1.79183905 |
\( -2647558 a^{4} - 4731364 a^{3} + 3202070 a^{2} + 4021669 a - 2770285 \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 4\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 5 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( 4 a^{4} - 6 a^{3} - 14 a^{2} + 2 a - 3\) , \( -7 a^{3} + 5 a^{2} + 14 a - 5\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+5a+3\right){x}^{2}+\left(4a^{4}-6a^{3}-14a^{2}+2a-3\right){x}-7a^{3}+5a^{2}+14a-5$ |
27.2-b1 |
27.2-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$47.98596$ |
$(-a^4+a^3+4a^2-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.671729300$ |
$300.0684748$ |
2.60942836 |
\( -94651371965 a^{4} + 115679364825 a^{3} + 428362635873 a^{2} - 245209014322 a - 76788326175 \) |
\( \bigl[2 a^{4} - a^{3} - 10 a^{2} - 2 a + 5\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a + 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} - 2 a + 4\) , \( 16 a^{4} - 2 a^{3} - 99 a^{2} - 29 a + 72\) , \( 471 a^{4} - 115 a^{3} - 2792 a^{2} - 738 a + 2032\bigr] \) |
${y}^2+\left(2a^{4}-a^{3}-10a^{2}-2a+5\right){x}{y}+\left(2a^{4}-a^{3}-10a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a+1\right){x}^{2}+\left(16a^{4}-2a^{3}-99a^{2}-29a+72\right){x}+471a^{4}-115a^{3}-2792a^{2}-738a+2032$ |
27.2-b2 |
27.2-b |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{11} \) |
$47.98596$ |
$(-a^4+a^3+4a^2-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.223909766$ |
$8101.848820$ |
2.60942836 |
\( -2647558 a^{4} - 4731364 a^{3} + 3202070 a^{2} + 4021669 a - 2770285 \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 2\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 2\) , \( a^{4} - 5 a^{2} - 2 a + 1\) , \( a^{4} + 2 a^{3} - 2 a^{2} - 6 a - 5\) , \( 3 a^{3} + 5 a^{2}\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+2\right){x}{y}+\left(a^{4}-5a^{2}-2a+1\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+3a+2\right){x}^{2}+\left(a^{4}+2a^{3}-2a^{2}-6a-5\right){x}+3a^{3}+5a^{2}$ |
29.1-a1 |
29.1-a |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$48.33009$ |
$(a^4-a^3-5a^2+2a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.108154679$ |
$3017.769283$ |
4.22534392 |
\( -\frac{43324}{29} a^{4} + \frac{38712}{29} a^{3} + \frac{253090}{29} a^{2} - \frac{82217}{29} a - \frac{246315}{29} \) |
\( \bigl[a^{4} - 6 a^{2} - 2 a + 4\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a + 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} - 7 a + 10\) , \( 5 a^{4} - 5 a^{3} - 22 a^{2} + a + 11\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-2a+4\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a+1\right){x}^{2}+\left(2a^{4}-a^{3}-9a^{2}-7a+10\right){x}+5a^{4}-5a^{3}-22a^{2}+a+11$ |
33.1-a1 |
33.1-a |
$1$ |
$1$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{6} \cdot 11 \) |
$48.95863$ |
$(-a^4+a^3+4a^2-1), (a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.061006185$ |
$1873.798596$ |
2.95976677 |
\( -\frac{11668154}{297} a^{4} + \frac{2666396}{297} a^{3} + \frac{7711012}{33} a^{2} + \frac{19140637}{297} a - \frac{5671498}{33} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - 5 a^{2} - 2 a + 1\) , \( 0\) , \( -3 a^{4} + 2 a^{3} + 20 a^{2} + 5 a - 12\) , \( a^{4} + 3 a^{3} - 5 a^{2} - 9 a + 7\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}={x}^{3}+\left(a^{4}-5a^{2}-2a+1\right){x}^{2}+\left(-3a^{4}+2a^{3}+20a^{2}+5a-12\right){x}+a^{4}+3a^{3}-5a^{2}-9a+7$ |
41.1-a1 |
41.1-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( -41 \) |
$50.03296$ |
$(a^4-a^3-4a^2-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$51.78983273$ |
1.20683453 |
\( \frac{59241130855}{41} a^{4} + \frac{44471870612}{41} a^{3} - \frac{322206588894}{41} a^{2} - \frac{420077877001}{41} a - \frac{78815079297}{41} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( a\) , \( 17 a^{4} - 13 a^{3} - 88 a^{2} + 7 a + 48\) , \( 35 a^{4} - 34 a^{3} - 170 a^{2} + 48 a + 64\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(17a^{4}-13a^{3}-88a^{2}+7a+48\right){x}+35a^{4}-34a^{3}-170a^{2}+48a+64$ |
41.1-a2 |
41.1-a |
$2$ |
$3$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{3} \) |
$50.03296$ |
$(a^4-a^3-4a^2-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1398.325483$ |
1.20683453 |
\( -\frac{691772024}{68921} a^{4} + \frac{162176403}{68921} a^{3} + \frac{4143591114}{68921} a^{2} + \frac{1065593113}{68921} a - \frac{3109463052}{68921} \) |
\( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 4\) , \( -a^{3} + 3 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( 21 a^{4} + 21 a^{3} - 116 a^{2} - 175 a - 35\) , \( 228 a^{4} + 176 a^{3} - 1241 a^{2} - 1639 a - 310\bigr] \) |
${y}^2+\left(2a^{4}-2a^{3}-9a^{2}+3a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(-a^{3}+3a+2\right){x}^{2}+\left(21a^{4}+21a^{3}-116a^{2}-175a-35\right){x}+228a^{4}+176a^{3}-1241a^{2}-1639a-310$ |
41.1-b1 |
41.1-b |
$2$ |
$7$ |
5.5.149169.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( -41 \) |
$50.03296$ |
$(a^4-a^3-4a^2-1)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 1 \) |
$0.549655901$ |
$16152.28665$ |
2.34563020 |
\( \frac{22984958}{41} a^{4} - \frac{44183985}{41} a^{3} - \frac{63584043}{41} a^{2} + \frac{45642697}{41} a + \frac{13164186}{41} \) |
\( \bigl[a^{4} - 6 a^{2} - 3 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a\) , \( a^{4} - 5 a^{2} - 3 a + 1\) , \( -3 a^{4} + 3 a^{3} + 12 a^{2} - 8 a - 2\) , \( 3 a^{4} - 2 a^{3} - 13 a^{2} + 2 a + 2\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-3a+4\right){x}{y}+\left(a^{4}-5a^{2}-3a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a\right){x}^{2}+\left(-3a^{4}+3a^{3}+12a^{2}-8a-2\right){x}+3a^{4}-2a^{3}-13a^{2}+2a+2$ |
*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.