| 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 |
| 2.1-a1 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.149031086$ |
$3531.894809$ |
1.56529439 |
\( -\frac{360736882681}{4} a^{4} - \frac{262280314891}{4} a^{3} + \frac{1973011873779}{4} a^{2} + \frac{897847656455}{2} a - \frac{494693250049}{4} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 8 a + 5\) , \( a^{4} - 5 a^{2} - a + 2\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 7 a + 5\) , \( -476 a^{4} - 107 a^{3} + 2829 a^{2} + 1102 a - 2137\) , \( 7162 a^{4} + 1592 a^{3} - 42633 a^{2} - 16678 a + 32098\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-8a+5\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-7a+5\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+2\right){x}^{2}+\left(-476a^{4}-107a^{3}+2829a^{2}+1102a-2137\right){x}+7162a^{4}+1592a^{3}-42633a^{2}-16678a+32098$ |
| 2.1-a2 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.074515543$ |
$14127.57923$ |
1.56529439 |
\( -\frac{1113017}{8} a^{4} - 98539 a^{3} + \frac{6060087}{8} a^{2} + \frac{5441917}{8} a - \frac{350793}{2} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 4\) , \( -a^{3} + 6 a\) , \( a^{3} - 5 a\) , \( -3 a^{4} - 6 a^{3} + 3 a^{2} + 5 a + 3\) , \( -2 a^{4} - 8 a^{3} - 2 a^{2} + 12 a - 2\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+4\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{3}+6a\right){x}^{2}+\left(-3a^{4}-6a^{3}+3a^{2}+5a+3\right){x}-2a^{4}-8a^{3}-2a^{2}+12a-2$ |
| 2.1-a3 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{12} \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.149031086$ |
$1765.947404$ |
1.56529439 |
\( \frac{5819557}{16} a^{4} - \frac{47608727}{64} a^{3} - \frac{2623955}{4} a^{2} + \frac{61990349}{64} a - \frac{10935257}{64} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 7 a + 6\) , \( -2 a^{4} - a^{3} + 12 a^{2} + 7 a - 6\) , \( a^{2} - a - 1\) , \( -3 a^{4} - 2 a^{3} + 17 a^{2} + 15 a - 3\) , \( -a^{4} - a^{3} + 6 a^{2} + 9 a - 3\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-7a+6\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+12a^{2}+7a-6\right){x}^{2}+\left(-3a^{4}-2a^{3}+17a^{2}+15a-3\right){x}-a^{4}-a^{3}+6a^{2}+9a-3$ |
| 2.1-a4 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.149031086$ |
$14127.57923$ |
1.56529439 |
\( \frac{20633}{4} a^{4} + \frac{54007}{4} a^{3} - \frac{3087}{4} a^{2} - \frac{25705}{2} a + \frac{11349}{4} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 4\) , \( -a^{3} + 4 a\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( 5 a^{4} + a^{3} - 30 a^{2} - 12 a + 25\) , \( 45 a^{4} + 10 a^{3} - 268 a^{2} - 104 a + 202\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+4\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(5a^{4}+a^{3}-30a^{2}-12a+25\right){x}+45a^{4}+10a^{3}-268a^{2}-104a+202$ |
| 2.1-a5 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.223546629$ |
$4709.193078$ |
1.56529439 |
\( \frac{5268575}{2} a^{4} + 5529116 a^{3} - \frac{3204937}{2} a^{2} - \frac{9225941}{2} a + 1342700 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 7 a - 2\) , \( a^{2} - 2\) , \( -8 a^{4} + 12 a^{3} + 20 a^{2} - 13 a\) , \( 36 a^{4} - 69 a^{3} - 72 a^{2} + 82 a - 15\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+7a-2\right){x}^{2}+\left(-8a^{4}+12a^{3}+20a^{2}-13a\right){x}+36a^{4}-69a^{3}-72a^{2}+82a-15$ |
| 2.1-a6 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.447093259$ |
$4709.193078$ |
1.56529439 |
\( -\frac{5733641753}{2} a^{4} + \frac{7265797921}{2} a^{3} + \frac{25194475581}{2} a^{2} - 13096674589 a + \frac{4524575883}{2} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 8 a + 5\) , \( -a^{4} - a^{3} + 6 a^{2} + 7 a - 4\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 1\) , \( 7 a^{4} - 22 a^{3} - 24 a^{2} + 95 a - 19\) , \( -88 a^{4} + 88 a^{3} + 399 a^{2} - 290 a + 44\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-8a+5\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+7a-4\right){x}^{2}+\left(7a^{4}-22a^{3}-24a^{2}+95a-19\right){x}-88a^{4}+88a^{3}+399a^{2}-290a+44$ |
| 2.1-a7 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.447093259$ |
$588.6491348$ |
1.56529439 |
\( 24606857042 a^{4} + \frac{21946855981}{4} a^{3} - 146420472864 a^{2} - \frac{229030250247}{4} a + \frac{441126538691}{4} \) |
\( \bigl[a\) , \( a^{4} + a^{3} - 7 a^{2} - 6 a + 4\) , \( a + 1\) , \( a^{4} - 8 a^{2} - 6 a + 3\) , \( -a^{3} - 2 a^{2} - a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-6a+4\right){x}^{2}+\left(a^{4}-8a^{2}-6a+3\right){x}-a^{3}-2a^{2}-a$ |
| 2.1-a8 |
2.1-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$40.25688$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.447093259$ |
$1177.298269$ |
1.56529439 |
\( \frac{671259209236651}{2} a^{4} + \frac{1585716545454235}{2} a^{3} - \frac{265769034450063}{2} a^{2} - 647038206149073 a + \frac{282773793409825}{2} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 6 a + 3\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 7 a + 6\) , \( -38 a^{4} - 28 a^{3} + 243 a^{2} + 175 a - 231\) , \( -20 a^{4} - 2 a^{3} + 106 a^{2} + 22 a - 64\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-6a+3\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-7a+6\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-38a^{4}-28a^{3}+243a^{2}+175a-231\right){x}-20a^{4}-2a^{3}+106a^{2}+22a-64$ |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$46.24302$ |
$(-a^4+5a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.203739794$ |
$573.3045559$ |
2.77883427 |
\( \frac{15702711}{2} a^{4} - 9948727 a^{3} - \frac{138002515}{4} a^{2} + 35864810 a - \frac{24773265}{4} \) |
\( \bigl[a^{2} - 1\) , \( -a^{4} + 6 a^{2} + a - 5\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 8 a + 5\) , \( 3 a^{4} - 15 a^{2} - 5 a + 10\) , \( -a^{4} + 4 a^{3} + 2 a^{2} - 9 a - 4\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-8a+5\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-5\right){x}^{2}+\left(3a^{4}-15a^{2}-5a+10\right){x}-a^{4}+4a^{3}+2a^{2}-9a-4$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{18} \) |
$46.24302$ |
$(-a^4+5a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.611219384$ |
$191.1015186$ |
2.77883427 |
\( \frac{12346935}{64} a^{4} + \frac{9120375}{64} a^{3} - \frac{16855411}{16} a^{2} - \frac{62225409}{64} a + \frac{16133841}{64} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 3\) , \( -a^{4} + 6 a^{2} + 2 a - 4\) , \( a^{4} - 5 a^{2} - a + 2\) , \( a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a - 2\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+3\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+2a-4\right){x}^{2}+a{x}+a^{4}-2a^{3}-3a^{2}+6a-2$ |
| 9.1-a1 |
9.1-a |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$189.1702335$ |
1.80017274 |
\( 379398215 a^{4} - \frac{2465388119}{3} a^{3} - 535395406 a^{2} + \frac{2729751257}{3} a - \frac{504670720}{3} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{4} + a^{3} - 5 a^{2} - 7 a + 2\) , \( -a^{4} - a^{3} + 7 a^{2} + 9 a - 2\) , \( 11 a^{4} + 8 a^{3} - 59 a^{2} - 52 a + 13\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-a^{4}-a^{3}+7a^{2}+9a-2\right){x}+11a^{4}+8a^{3}-59a^{2}-52a+13$ |
| 9.1-a2 |
9.1-a |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{16} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6053.447474$ |
1.80017274 |
\( -\frac{14029042646}{6561} a^{4} + \frac{504135643}{6561} a^{3} + \frac{71802042116}{6561} a^{2} + \frac{17443271860}{6561} a - \frac{7435316386}{6561} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( a^{3} - 5 a - 1\) , \( 77 a^{4} + 19 a^{3} - 457 a^{2} - 189 a + 336\) , \( -370 a^{4} - 83 a^{3} + 2203 a^{2} + 863 a - 1664\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+3\right){x}^{2}+\left(77a^{4}+19a^{3}-457a^{2}-189a+336\right){x}-370a^{4}-83a^{3}+2203a^{2}+863a-1664$ |
| 9.1-a3 |
9.1-a |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$12106.89494$ |
1.80017274 |
\( -\frac{9970}{81} a^{4} + \frac{7973}{81} a^{3} + \frac{22459}{81} a^{2} - \frac{19459}{81} a + \frac{267928}{81} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 6 a + 3\) , \( a^{4} + a^{3} - 7 a^{2} - 4 a + 4\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 8 a + 6\) , \( 3 a^{4} - a^{3} - 14 a^{2} - 7 a + 3\) , \( 2 a^{3} - 2 a^{2} - 6 a - 1\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-6a+3\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-8a+6\right){y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-4a+4\right){x}^{2}+\left(3a^{4}-a^{3}-14a^{2}-7a+3\right){x}+2a^{3}-2a^{2}-6a-1$ |
| 9.1-a4 |
9.1-a |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6053.447474$ |
1.80017274 |
\( \frac{61346}{9} a^{4} + \frac{13228}{9} a^{3} - \frac{362945}{9} a^{2} - \frac{46931}{3} a + \frac{280109}{9} \) |
\( \bigl[-a^{4} + 6 a^{2} + 2 a - 4\) , \( -a^{3} + 6 a\) , \( a^{4} + a^{3} - 6 a^{2} - 6 a + 4\) , \( a^{3} - a^{2} - 4 a + 9\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a - 1\bigr] \) |
${y}^2+\left(-a^{4}+6a^{2}+2a-4\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-6a+4\right){y}={x}^{3}+\left(-a^{3}+6a\right){x}^{2}+\left(a^{3}-a^{2}-4a+9\right){x}+a^{4}-a^{3}-4a^{2}+5a-1$ |
| 9.1-a5 |
9.1-a |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$1513.361868$ |
1.80017274 |
\( \frac{14615197}{9} a^{4} + \frac{3264680}{9} a^{3} - \frac{86637841}{9} a^{2} - \frac{11279668}{3} a + \frac{65402251}{9} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 1\) , \( 27 a^{4} + 18 a^{3} - 145 a^{2} - 128 a + 35\) , \( 167 a^{4} + 124 a^{3} - 914 a^{2} - 840 a + 224\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(27a^{4}+18a^{3}-145a^{2}-128a+35\right){x}+167a^{4}+124a^{3}-914a^{2}-840a+224$ |
| 9.1-a6 |
9.1-a |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$47.29255839$ |
1.80017274 |
\( 9666992275461 a^{4} + \frac{6479548121105}{3} a^{3} - 57514503503934 a^{2} - \frac{67513400819555}{3} a + \frac{129923941271782}{3} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 3\) , \( -3 a^{4} - a^{3} + 17 a^{2} + 9 a - 9\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 3\) , \( -85 a^{4} + 102 a^{3} + 378 a^{2} - 363 a + 56\) , \( 7881 a^{4} - 9986 a^{3} - 34636 a^{2} + 36012 a - 6222\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+3\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+3\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+17a^{2}+9a-9\right){x}^{2}+\left(-85a^{4}+102a^{3}+378a^{2}-363a+56\right){x}+7881a^{4}-9986a^{3}-34636a^{2}+36012a-6222$ |
| 9.1-b1 |
9.1-b |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$635.2381280$ |
1.51125568 |
\( -\frac{22117836205}{81} a^{4} - \frac{16099521793}{81} a^{3} + \frac{120988245247}{81} a^{2} + \frac{110184914987}{81} a - \frac{30385935743}{81} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 8 a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{3} - 4 a - 1\) , \( -a^{4} - 4 a^{3} + 5 a^{2} + 19 a + 11\) , \( -6 a^{4} + a^{3} + 22 a^{2} + 19 a + 5\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-8a+5\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){x}^{2}+\left(-a^{4}-4a^{3}+5a^{2}+19a+11\right){x}-6a^{4}+a^{3}+22a^{2}+19a+5$ |
| 9.1-b2 |
9.1-b |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$5081.905024$ |
1.51125568 |
\( -\frac{1555136}{9} a^{4} + \frac{1872176}{9} a^{3} + \frac{7009793}{9} a^{2} - 750584 a + \frac{1242976}{9} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 7 a + 6\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( a^{4} - 5 a^{3} + 22 a - 17\) , \( 27 a^{4} - 31 a^{3} - 122 a^{2} + 109 a - 11\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-7a+6\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){x}^{2}+\left(a^{4}-5a^{3}+22a-17\right){x}+27a^{4}-31a^{3}-122a^{2}+109a-11$ |
| 9.1-b3 |
9.1-b |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$10163.81004$ |
1.51125568 |
\( 30063964 a^{4} + \frac{20130883}{3} a^{3} - 178886145 a^{2} - \frac{209975122}{3} a + \frac{404097641}{3} \) |
\( \bigl[a\) , \( 3 a^{4} + a^{3} - 17 a^{2} - 10 a + 8\) , \( a^{3} - 4 a - 1\) , \( -3 a^{4} - 3 a^{3} + 15 a^{2} + 19 a + 3\) , \( 42 a^{4} + 30 a^{3} - 230 a^{2} - 206 a + 60\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(3a^{4}+a^{3}-17a^{2}-10a+8\right){x}^{2}+\left(-3a^{4}-3a^{3}+15a^{2}+19a+3\right){x}+42a^{4}+30a^{3}-230a^{2}-206a+60$ |
| 9.1-b4 |
9.1-b |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$46.79090$ |
$(a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$635.2381280$ |
1.51125568 |
\( -254535204878 a^{4} + \frac{967253950400}{3} a^{3} + 1119848235074 a^{2} - \frac{3492072062591}{3} a + \frac{603193936276}{3} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 7 a + 6\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( 76 a^{4} - 110 a^{3} - 320 a^{2} + 412 a - 112\) , \( 1085 a^{4} - 1407 a^{3} - 4735 a^{2} + 5108 a - 972\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-7a+6\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){x}^{2}+\left(76a^{4}-110a^{3}-320a^{2}+412a-112\right){x}+1085a^{4}-1407a^{3}-4735a^{2}+5108a-972$ |
| 16.1-a1 |
16.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$695.0050258$ |
1.65344340 |
\( \frac{158535760089186293}{8} a^{4} - \frac{325239251489783797}{8} a^{3} - \frac{283979794943573959}{8} a^{2} + \frac{212027206539935735}{4} a - \frac{77277226175817715}{8} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( -2 a^{4} - a^{3} + 11 a^{2} + 8 a - 4\) , \( a^{4} + a^{3} - 6 a^{2} - 6 a + 3\) , \( -26 a^{4} - 12 a^{3} + 137 a^{2} + 57 a - 106\) , \( 227 a^{4} + 142 a^{3} - 1212 a^{2} - 825 a + 604\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-6a+3\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+11a^{2}+8a-4\right){x}^{2}+\left(-26a^{4}-12a^{3}+137a^{2}+57a-106\right){x}+227a^{4}+142a^{3}-1212a^{2}-825a+604$ |
| 16.1-a2 |
16.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$2780.020103$ |
1.65344340 |
\( \frac{962328151}{32} a^{4} - \frac{246775477}{4} a^{3} - \frac{1723846041}{32} a^{2} + \frac{2573987245}{32} a - \frac{117237075}{8} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( -2 a^{4} - a^{3} + 11 a^{2} + 8 a - 4\) , \( a^{4} + a^{3} - 6 a^{2} - 6 a + 3\) , \( -16 a^{4} - 12 a^{3} + 87 a^{2} + 77 a - 26\) , \( -23 a^{4} - 18 a^{3} + 124 a^{2} + 119 a - 26\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-6a+3\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+11a^{2}+8a-4\right){x}^{2}+\left(-16a^{4}-12a^{3}+87a^{2}+77a-26\right){x}-23a^{4}-18a^{3}+124a^{2}+119a-26$ |
| 16.1-a3 |
16.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{17} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2780.020103$ |
1.65344340 |
\( -\frac{269057}{16} a^{4} - \frac{121967}{8} a^{3} + \frac{385021}{4} a^{2} + \frac{366875}{4} a - \frac{388717}{16} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 6 a + 3\) , \( -2 a^{4} - a^{3} + 12 a^{2} + 8 a - 6\) , \( a^{2} - 1\) , \( 4 a^{4} + 2 a^{3} - 22 a^{2} - 14 a + 11\) , \( -a^{4} + 5 a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-6a+3\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-2a^{4}-a^{3}+12a^{2}+8a-6\right){x}^{2}+\left(4a^{4}+2a^{3}-22a^{2}-14a+11\right){x}-a^{4}+5a^{2}+2a-3$ |
| 16.1-a4 |
16.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{23} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$347.5025129$ |
1.65344340 |
\( -\frac{8591847}{256} a^{4} + \frac{90573865}{1024} a^{3} + \frac{5633173}{32} a^{2} - \frac{261164355}{1024} a + \frac{70817319}{1024} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 3\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 4\) , \( 2176 a^{4} - 2760 a^{3} - 9558 a^{2} + 9947 a - 1720\) , \( 112480 a^{4} - 142538 a^{3} - 494253 a^{2} + 513852 a - 88763\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+3\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(2176a^{4}-2760a^{3}-9558a^{2}+9947a-1720\right){x}+112480a^{4}-142538a^{3}-494253a^{2}+513852a-88763$ |
| 16.1-b1 |
16.1-b |
$2$ |
$3$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{15} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$228.1356006$ |
3.25645965 |
\( \frac{2617619481}{8} a^{4} + \frac{1941304231}{8} a^{3} - \frac{14362839485}{8} a^{2} - \frac{13143161071}{8} a + \frac{3609570763}{8} \) |
\( \bigl[-a^{4} + 6 a^{2} + a - 3\) , \( 2 a^{4} - 11 a^{2} - 3 a + 7\) , \( a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( 10 a^{4} + 3 a^{3} - 56 a^{2} - 29 a + 25\) , \( 18 a^{4} + 4 a^{3} - 96 a^{2} - 45 a + 26\bigr] \) |
${y}^2+\left(-a^{4}+6a^{2}+a-3\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){y}={x}^{3}+\left(2a^{4}-11a^{2}-3a+7\right){x}^{2}+\left(10a^{4}+3a^{3}-56a^{2}-29a+25\right){x}+18a^{4}+4a^{3}-96a^{2}-45a+26$ |
| 16.1-b2 |
16.1-b |
$2$ |
$3$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{5} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$684.4068018$ |
3.25645965 |
\( \frac{4020609943}{2} a^{4} + \frac{9451158223}{2} a^{3} - 830078877 a^{2} - \frac{7651436295}{2} a + 837700678 \) |
\( \bigl[1\) , \( -a^{3} + 6 a + 1\) , \( -a^{4} + 6 a^{2} + 2 a - 3\) , \( 20 a^{4} + 4 a^{3} - 122 a^{2} - 48 a + 97\) , \( -295 a^{4} - 65 a^{3} + 1758 a^{2} + 685 a - 1330\bigr] \) |
${y}^2+{x}{y}+\left(-a^{4}+6a^{2}+2a-3\right){y}={x}^{3}+\left(-a^{3}+6a+1\right){x}^{2}+\left(20a^{4}+4a^{3}-122a^{2}-48a+97\right){x}-295a^{4}-65a^{3}+1758a^{2}+685a-1330$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{11} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.007567469$ |
$12802.73653$ |
2.30491476 |
\( -\frac{621804947}{16} a^{4} + \frac{640871739}{8} a^{3} + \frac{1093597293}{16} a^{2} - \frac{1648523931}{16} a + \frac{150377623}{8} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( -a^{4} - a^{3} + 7 a^{2} + 6 a - 4\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 8 a + 6\) , \( -8 a^{4} - 3 a^{3} + 37 a^{2} + 42 a - 8\) , \( -15 a^{4} - 14 a^{3} + 91 a^{2} + 74 a - 24\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-8a+6\right){y}={x}^{3}+\left(-a^{4}-a^{3}+7a^{2}+6a-4\right){x}^{2}+\left(-8a^{4}-3a^{3}+37a^{2}+42a-8\right){x}-15a^{4}-14a^{3}+91a^{2}+74a-24$ |
| 16.1-d1 |
16.1-d |
$2$ |
$3$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{27} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.015755513$ |
$1184.572154$ |
5.32815334 |
\( -\frac{75390185}{4096} a^{4} - \frac{38005671}{2048} a^{3} + \frac{517596279}{4096} a^{2} + \frac{460040647}{4096} a - \frac{278332199}{2048} \) |
\( \bigl[a^{2} - 2\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 7 a + 8\) , \( -a^{4} + 6 a^{2} + a - 4\) , \( -8 a^{4} - 2 a^{3} + 47 a^{2} + 20 a - 34\) , \( -48 a^{4} - 11 a^{3} + 285 a^{2} + 112 a - 215\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(-a^{4}+6a^{2}+a-4\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-7a+8\right){x}^{2}+\left(-8a^{4}-2a^{3}+47a^{2}+20a-34\right){x}-48a^{4}-11a^{3}+285a^{2}+112a-215$ |
| 16.1-d2 |
16.1-d |
$2$ |
$3$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{17} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.005251837$ |
$3553.716462$ |
5.32815334 |
\( \frac{1051953}{16} a^{4} + \frac{446585}{8} a^{3} - \frac{5367317}{16} a^{2} - \frac{5012583}{16} a + 86773 \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 1\) , \( 1\) , \( -9 a^{4} + 5 a^{3} + 48 a^{2} - 19 a + 2\) , \( -38 a^{4} + 53 a^{3} + 145 a^{2} - 143 a + 24\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-9a^{4}+5a^{3}+48a^{2}-19a+2\right){x}-38a^{4}+53a^{3}+145a^{2}-143a+24$ |
| 16.1-e1 |
16.1-e |
$4$ |
$6$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.874024112$ |
$228.6687864$ |
2.37739691 |
\( -\frac{2069523329789865087}{64} a^{4} - \frac{753200257967087377}{32} a^{3} + \frac{11320635058141316483}{64} a^{2} + \frac{5154891708081759601}{32} a - \frac{1421576389293895491}{32} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 2 a^{4} - 11 a^{2} - 3 a + 7\) , \( 0\) , \( -15 a^{4} + 2 a^{3} + 98 a^{2} + 20 a - 84\) , \( 33 a^{4} + 23 a^{3} - 171 a^{2} - 127 a + 75\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}={x}^{3}+\left(2a^{4}-11a^{2}-3a+7\right){x}^{2}+\left(-15a^{4}+2a^{3}+98a^{2}+20a-84\right){x}+33a^{4}+23a^{3}-171a^{2}-127a+75$ |
| 16.1-e2 |
16.1-e |
$4$ |
$6$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{15} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.582682741$ |
$686.0063592$ |
2.37739691 |
\( -\frac{4083203}{16} a^{4} + \frac{519035989}{16} a^{3} + \frac{584541887}{16} a^{2} - \frac{935812163}{16} a + \frac{86216709}{8} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 7 a + 6\) , \( -a^{4} + 5 a^{2} + 2 a - 2\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 4\) , \( 7 a^{4} + 6 a^{3} - 39 a^{2} - 40 a + 6\) , \( 97 a^{4} + 71 a^{3} - 531 a^{2} - 485 a + 132\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-7a+6\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+4\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-2\right){x}^{2}+\left(7a^{4}+6a^{3}-39a^{2}-40a+6\right){x}+97a^{4}+71a^{3}-531a^{2}-485a+132$ |
| 16.1-e3 |
16.1-e |
$4$ |
$6$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{37} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.748048224$ |
$228.6687864$ |
2.37739691 |
\( \frac{85956122371}{1024} a^{4} + \frac{250269775375}{4096} a^{3} - \frac{1880776910419}{4096} a^{2} - \frac{1712840375789}{4096} a + \frac{472357692549}{4096} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( -a^{4} + 6 a^{2} + a - 4\) , \( 14 a^{4} + 5 a^{3} - 83 a^{2} - 41 a + 58\) , \( 37 a^{4} + 15 a^{3} - 214 a^{2} - 121 a + 126\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){x}{y}+\left(-a^{4}+6a^{2}+a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(14a^{4}+5a^{3}-83a^{2}-41a+58\right){x}+37a^{4}+15a^{3}-214a^{2}-121a+126$ |
| 16.1-e4 |
16.1-e |
$4$ |
$6$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$49.56204$ |
$(-a^3+a^2+4a-2), (-a^4+5a^2+a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.291341370$ |
$686.0063592$ |
2.37739691 |
\( \frac{23694812177}{8} a^{4} - \frac{268231427}{2} a^{3} - \frac{129358967833}{8} a^{2} - \frac{41170209631}{8} a + \frac{46136423929}{4} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( a^{3} - 5 a\) , \( 18 a^{4} + 15 a^{3} - 99 a^{2} - 108 a + 20\) , \( 76 a^{4} + 55 a^{3} - 413 a^{2} - 369 a + 121\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){x}^{2}+\left(18a^{4}+15a^{3}-99a^{2}-108a+20\right){x}+76a^{4}+55a^{3}-413a^{2}-369a+121$ |
| 16.2-a1 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{15} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$0.414802010$ |
$373.5187420$ |
3.68599413 |
\( -\frac{360736882681}{4} a^{4} - \frac{262280314891}{4} a^{3} + \frac{1973011873779}{4} a^{2} + \frac{897847656455}{2} a - \frac{494693250049}{4} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 8 a + 6\) , \( -2 a^{4} + 11 a^{2} + 3 a - 5\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 3\) , \( a^{4} - 34 a^{3} + 24 a^{2} + 153 a - 98\) , \( 97 a^{4} - 202 a^{3} - 354 a^{2} + 804 a - 332\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-8a+6\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+3\right){y}={x}^{3}+\left(-2a^{4}+11a^{2}+3a-5\right){x}^{2}+\left(a^{4}-34a^{3}+24a^{2}+153a-98\right){x}+97a^{4}-202a^{3}-354a^{2}+804a-332$ |
| 16.2-a2 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{18} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$0.207401005$ |
$5976.299872$ |
3.68599413 |
\( -\frac{1113017}{8} a^{4} - 98539 a^{3} + \frac{6060087}{8} a^{2} + \frac{5441917}{8} a - \frac{350793}{2} \) |
\( \bigl[2 a^{4} + a^{3} - 11 a^{2} - 8 a + 6\) , \( -2 a^{4} + 11 a^{2} + 3 a - 5\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 3\) , \( -4 a^{4} - 4 a^{3} + 24 a^{2} + 23 a - 13\) , \( -a^{4} - 7 a^{3} + 9 a^{2} + 35 a - 11\bigr] \) |
${y}^2+\left(2a^{4}+a^{3}-11a^{2}-8a+6\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+3\right){y}={x}^{3}+\left(-2a^{4}+11a^{2}+3a-5\right){x}^{2}+\left(-4a^{4}-4a^{3}+24a^{2}+23a-13\right){x}-a^{4}-7a^{3}+9a^{2}+35a-11$ |
| 16.2-a3 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{24} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.103700502$ |
$2988.149936$ |
3.68599413 |
\( \frac{5819557}{16} a^{4} - \frac{47608727}{64} a^{3} - \frac{2623955}{4} a^{2} + \frac{61990349}{64} a - \frac{10935257}{64} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{4} + a^{3} - 5 a^{2} - 8 a\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 7 a + 5\) , \( -21 a^{4} + 16 a^{3} + 99 a^{2} - 48 a + 2\) , \( 565 a^{4} - 707 a^{3} - 2487 a^{2} + 2537 a - 438\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(2a^{4}+a^{3}-11a^{2}-7a+5\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-8a\right){x}^{2}+\left(-21a^{4}+16a^{3}+99a^{2}-48a+2\right){x}+565a^{4}-707a^{3}-2487a^{2}+2537a-438$ |
| 16.2-a4 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{15} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.103700502$ |
$5976.299872$ |
3.68599413 |
\( \frac{20633}{4} a^{4} + \frac{54007}{4} a^{3} - \frac{3087}{4} a^{2} - \frac{25705}{2} a + \frac{11349}{4} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 6 a + 4\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 9 a + 5\) , \( a^{2} - a - 2\) , \( 2 a^{4} - a^{3} - 10 a^{2} - a + 9\) , \( 2 a^{4} - a^{3} - 8 a^{2} - 3 a + 2\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-6a+4\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(2a^{4}+a^{3}-11a^{2}-9a+5\right){x}^{2}+\left(2a^{4}-a^{3}-10a^{2}-a+9\right){x}+2a^{4}-a^{3}-8a^{2}-3a+2$ |
| 16.2-a5 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{14} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$0.622203015$ |
$1992.099957$ |
3.68599413 |
\( \frac{5268575}{2} a^{4} + 5529116 a^{3} - \frac{3204937}{2} a^{2} - \frac{9225941}{2} a + 1342700 \) |
\( \bigl[a + 1\) , \( a^{3} - 4 a - 2\) , \( -a^{4} + 6 a^{2} + a - 4\) , \( 4 a^{4} + 5 a^{3} - 20 a^{2} - 35 a - 13\) , \( 31 a^{4} + 11 a^{3} - 185 a^{2} - 108 a + 102\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{4}+6a^{2}+a-4\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(4a^{4}+5a^{3}-20a^{2}-35a-13\right){x}+31a^{4}+11a^{3}-185a^{2}-108a+102$ |
| 16.2-a6 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{13} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.311101507$ |
$1992.099957$ |
3.68599413 |
\( -\frac{5733641753}{2} a^{4} + \frac{7265797921}{2} a^{3} + \frac{25194475581}{2} a^{2} - 13096674589 a + \frac{4524575883}{2} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( a^{4} - 5 a^{2} - a + 3\) , \( -13 a^{4} - 7 a^{3} + 70 a^{2} + 51 a - 14\) , \( 86 a^{4} + 63 a^{3} - 472 a^{2} - 432 a + 126\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-2\right){x}^{2}+\left(-13a^{4}-7a^{3}+70a^{2}+51a-14\right){x}+86a^{4}+63a^{3}-472a^{2}-432a+126$ |
| 16.2-a7 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{16} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.311101507$ |
$996.0499787$ |
3.68599413 |
\( 24606857042 a^{4} + \frac{21946855981}{4} a^{3} - 146420472864 a^{2} - \frac{229030250247}{4} a + \frac{441126538691}{4} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{4} - 5 a^{2} - a + 2\) , \( -a^{4} + 6 a^{2} + a - 4\) , \( -3 a^{4} + 3 a^{3} + 12 a^{2} + a - 8\) , \( -5 a^{4} + 9 a^{3} + 14 a^{2} - 16 a + 1\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(-a^{4}+6a^{2}+a-4\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+2\right){x}^{2}+\left(-3a^{4}+3a^{3}+12a^{2}+a-8\right){x}-5a^{4}+9a^{3}+14a^{2}-16a+1$ |
| 16.2-a8 |
16.2-a |
$8$ |
$12$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{13} \) |
$49.56204$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1.244406031$ |
$124.5062473$ |
3.68599413 |
\( \frac{671259209236651}{2} a^{4} + \frac{1585716545454235}{2} a^{3} - \frac{265769034450063}{2} a^{2} - 647038206149073 a + \frac{282773793409825}{2} \) |
\( \bigl[a + 1\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 7 a + 6\) , \( -a^{4} + 6 a^{2} + a - 4\) , \( 1218 a^{4} - 1545 a^{3} - 5354 a^{2} + 5573 a - 961\) , \( 8385 a^{4} - 10629 a^{3} - 36844 a^{2} + 38321 a - 6629\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{4}+6a^{2}+a-4\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-7a+6\right){x}^{2}+\left(1218a^{4}-1545a^{3}-5354a^{2}+5573a-961\right){x}+8385a^{4}-10629a^{3}-36844a^{2}+38321a-6629$ |
| 18.1-a1 |
18.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5138.097818$ |
1.52796628 |
\( \frac{223109852286277}{16} a^{4} - \frac{343285710381569}{12} a^{3} - \frac{399649202529939}{16} a^{2} + \frac{1790335204228169}{48} a - \frac{40782542959697}{6} \) |
\( \bigl[-a^{4} + 6 a^{2} + 2 a - 4\) , \( -a^{3} + 4 a + 2\) , \( a^{2} - 1\) , \( -2 a^{4} - 2 a^{3} + 8 a^{2} + 14 a + 4\) , \( -3 a^{4} - 3 a^{3} + 16 a^{2} + 17 a - 1\bigr] \) |
${y}^2+\left(-a^{4}+6a^{2}+2a-4\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-2a^{4}-2a^{3}+8a^{2}+14a+4\right){x}-3a^{4}-3a^{3}+16a^{2}+17a-1$ |
| 18.1-a2 |
18.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{32} \cdot 3^{8} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$321.1311136$ |
1.52796628 |
\( -\frac{26901091663}{331776} a^{4} - \frac{308036984377}{5308416} a^{3} + \frac{589166928637}{1327104} a^{2} + \frac{2131311367439}{5308416} a - \frac{600157966823}{5308416} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( a^{3} - 6 a\) , \( a^{4} - 5 a^{2} - a + 3\) , \( 20 a^{4} + 17 a^{3} - 114 a^{2} - 119 a + 33\) , \( 138 a^{4} + 105 a^{3} - 750 a^{2} - 698 a + 190\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(a^{3}-6a\right){x}^{2}+\left(20a^{4}+17a^{3}-114a^{2}-119a+33\right){x}+138a^{4}+105a^{3}-750a^{2}-698a+190$ |
| 18.1-a3 |
18.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$2569.048909$ |
1.52796628 |
\( \frac{2280793987}{576} a^{4} + \frac{2523857417}{2304} a^{3} - \frac{4320701807}{288} a^{2} - \frac{3736907897}{768} a + \frac{22943851687}{2304} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{4} - a^{3} + 5 a^{2} + 6 a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 1\) , \( -a^{4} - 6 a^{3} + 3 a^{2} + 17 a - 10\) , \( 6 a^{4} + 5 a^{3} - 13 a^{2} + 2 a - 5\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+6a-2\right){x}^{2}+\left(-a^{4}-6a^{3}+3a^{2}+17a-10\right){x}+6a^{4}+5a^{3}-13a^{2}+2a-5$ |
| 18.1-a4 |
18.1-a |
$4$ |
$4$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$321.1311136$ |
1.52796628 |
\( \frac{1094339694431163}{16} a^{4} + \frac{1477871030496689}{12} a^{3} - \frac{2039095540847757}{16} a^{2} - \frac{6690011001888521}{48} a + \frac{613664148950981}{6} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 6 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 2\) , \( -a^{4} + 6 a^{2} + 2 a - 3\) , \( 216 a^{4} + 215 a^{3} - 1262 a^{2} - 1259 a + 322\) , \( -2582 a^{4} - 2237 a^{3} + 14655 a^{2} + 13867 a - 3863\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-6a+3\right){x}{y}+\left(-a^{4}+6a^{2}+2a-3\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+2\right){x}^{2}+\left(216a^{4}+215a^{3}-1262a^{2}-1259a+322\right){x}-2582a^{4}-2237a^{3}+14655a^{2}+13867a-3863$ |
| 18.1-b1 |
18.1-b |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{4} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1599.747815$ |
0.951465232 |
\( -\frac{27191624263784304376283465}{9} a^{4} - \frac{39585421657664022888972527}{18} a^{3} + \frac{148742684123139921542973476}{9} a^{2} + \frac{30102450577541747607994545}{2} a - \frac{74712800737306094526912019}{18} \) |
\( \bigl[a\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 2\) , \( a + 1\) , \( 4851 a^{4} - 6147 a^{3} - 21318 a^{2} + 22160 a - 3822\) , \( -372469 a^{4} + 471992 a^{3} + 1636694 a^{2} - 1701534 a + 293893\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-6a^{2}-5a+2\right){x}^{2}+\left(4851a^{4}-6147a^{3}-21318a^{2}+22160a-3822\right){x}-372469a^{4}+471992a^{3}+1636694a^{2}-1701534a+293893$ |
| 18.1-b2 |
18.1-b |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$12.49802981$ |
0.951465232 |
\( \frac{2942849905251038}{3} a^{4} - \frac{8051565759827911}{4} a^{3} - \frac{5266676968322336}{3} a^{2} + \frac{31472318829152587}{12} a - \frac{1911881587553069}{4} \) |
\( \bigl[-a^{4} + 6 a^{2} + a - 3\) , \( -a^{4} - a^{3} + 5 a^{2} + 7 a - 2\) , \( a^{4} - 5 a^{2} - 2 a + 3\) , \( -5 a^{4} - a^{3} - 65 a^{2} - 107 a - 20\) , \( -241 a^{4} - 323 a^{3} + 485 a^{2} + 418 a - 285\bigr] \) |
${y}^2+\left(-a^{4}+6a^{2}+a-3\right){x}{y}+\left(a^{4}-5a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+7a-2\right){x}^{2}+\left(-5a^{4}-a^{3}-65a^{2}-107a-20\right){x}-241a^{4}-323a^{3}+485a^{2}+418a-285$ |
| 18.1-b3 |
18.1-b |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3199.495631$ |
0.951465232 |
\( -\frac{65722363502425}{81} a^{4} - \frac{191356533848437}{324} a^{3} + \frac{359512203460486}{81} a^{2} + \frac{1309641356622635}{324} a - \frac{361162816284479}{324} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 7 a + 1\) , \( 2 a^{4} + a^{3} - 12 a^{2} - 7 a + 8\) , \( a^{2} - 2\) , \( 4 a^{3} + 2 a^{2} - 22 a - 22\) , \( -48 a^{4} - 14 a^{3} + 282 a^{2} + 128 a - 196\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-7a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(2a^{4}+a^{3}-12a^{2}-7a+8\right){x}^{2}+\left(4a^{3}+2a^{2}-22a-22\right){x}-48a^{4}-14a^{3}+282a^{2}+128a-196$ |
| 18.1-b4 |
18.1-b |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{16} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1599.747815$ |
0.951465232 |
\( \frac{2765841154}{6561} a^{4} + \frac{4021833647}{13122} a^{3} - \frac{15133800235}{6561} a^{2} - \frac{27526823809}{13122} a + \frac{7658239531}{13122} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 3\) , \( 2 a^{4} + a^{3} - 11 a^{2} - 9 a + 6\) , \( a^{3} - 4 a - 1\) , \( 4 a^{4} - a^{3} - 18 a^{2} - 6 a + 12\) , \( -2 a^{4} - 5 a^{3} + 14 a^{2} + 20 a - 2\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(2a^{4}+a^{3}-11a^{2}-9a+6\right){x}^{2}+\left(4a^{4}-a^{3}-18a^{2}-6a+12\right){x}-2a^{4}-5a^{3}+14a^{2}+20a-2$ |
| 18.1-b5 |
18.1-b |
$6$ |
$8$ |
5.5.176684.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$50.14925$ |
$(-a^3+a^2+4a-2), (a^3-a^2-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$399.9369539$ |
0.951465232 |
\( \frac{939352033}{18} a^{4} - \frac{485291921}{144} a^{3} - \frac{10196952185}{36} a^{2} - \frac{1419731849}{16} a + \frac{29267106017}{144} \) |
\( \bigl[-a^{4} + 6 a^{2} + a - 3\) , \( -a^{4} - a^{3} + 5 a^{2} + 7 a - 2\) , \( a^{4} - 5 a^{2} - 2 a + 3\) , \( 10 a^{4} + 14 a^{3} - 55 a^{2} - 92 a - 25\) , \( -116 a^{4} - 64 a^{3} + 645 a^{2} + 449 a - 298\bigr] \) |
${y}^2+\left(-a^{4}+6a^{2}+a-3\right){x}{y}+\left(a^{4}-5a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+7a-2\right){x}^{2}+\left(10a^{4}+14a^{3}-55a^{2}-92a-25\right){x}-116a^{4}-64a^{3}+645a^{2}+449a-298$ |
*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.
