| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 4.1-a1 |
4.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{3} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$758.9865662$ |
3.562414336 |
\( -\frac{4921}{2} a^{3} + 6772 a^{2} + 1016 a - \frac{9321}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{2} - a - 3\) , \( -11 a^{3} + 18 a^{2} + 44 a - 40\) , \( 31 a^{3} - 49 a^{2} - 126 a + 103\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-11a^{3}+18a^{2}+44a-40\right){x}+31a^{3}-49a^{2}-126a+103$ |
| 4.1-a2 |
4.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$84.33184069$ |
3.562414336 |
\( -\frac{13274440865651}{8} a^{3} + \frac{36869954817925}{8} a^{2} + \frac{895143848177}{8} a - \frac{14988334856695}{8} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{2} - a - 3\) , \( 104 a^{3} - 162 a^{2} - 421 a + 325\) , \( -392 a^{3} + 641 a^{2} + 1565 a - 1383\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(104a^{3}-162a^{2}-421a+325\right){x}-392a^{3}+641a^{2}+1565a-1383$ |
| 4.1-a3 |
4.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{3} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$758.9865662$ |
3.562414336 |
\( \frac{5170795}{4} a^{3} - \frac{11305515}{4} a^{2} - \frac{18112897}{4} a + \frac{32436575}{4} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( 5 a^{3} - 27 a - 16\) , \( 15 a^{3} - 86 a - 48\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(5a^{3}-27a-16\right){x}+15a^{3}-86a-48$ |
| 4.1-a4 |
4.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$84.33184069$ |
3.562414336 |
\( -\frac{576237781537807354959}{64} a^{3} + \frac{159190226393205886841}{64} a^{2} + \frac{2996401580039519157509}{64} a + \frac{1592384258224686624515}{64} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 4 a\) , \( 0\) , \( -142 a^{3} - 239 a^{2} + 89 a + 107\) , \( 3213 a^{3} + 5278 a^{2} - 2141 a - 2437\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-142a^{3}-239a^{2}+89a+107\right){x}+3213a^{3}+5278a^{2}-2141a-2437$ |
| 4.1-b1 |
4.1-b |
$2$ |
$11$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{22} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.10.1 |
$1$ |
\( 1 \) |
$1$ |
$87.02407012$ |
0.816920374 |
\( \frac{96026345973}{2048} a^{3} - \frac{26829847203}{2048} a^{2} - \frac{500046449383}{2048} a - \frac{265678036177}{2048} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a\) , \( 67 a^{3} - 19 a^{2} - 349 a - 182\) , \( -463 a^{3} + 128 a^{2} + 2407 a + 1278\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(67a^{3}-19a^{2}-349a-182\right){x}-463a^{3}+128a^{2}+2407a+1278$ |
| 4.1-b2 |
4.1-b |
$2$ |
$11$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.10.2 |
$121$ |
\( 1 \) |
$1$ |
$0.719207191$ |
0.816920374 |
\( -58621608199599841261523685365125 a^{3} + \frac{186324765270697790904663848098547}{2} a^{2} + 238215298486610603874100648409004 a - \frac{397963624619871051990068501920911}{2} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a\) , \( -193 a^{3} - 484 a^{2} + 3676 a - 2802\) , \( -11222 a^{3} + 109824 a^{2} - 118878 a - 245314\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-193a^{3}-484a^{2}+3676a-2802\right){x}-11222a^{3}+109824a^{2}-118878a-245314$ |
| 4.1-c1 |
4.1-c |
$2$ |
$11$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{22} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{2} \) |
$1$ |
$305.8508628$ |
2.871111419 |
\( \frac{96026345973}{2048} a^{3} - \frac{26829847203}{2048} a^{2} - \frac{500046449383}{2048} a - \frac{265678036177}{2048} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( -a^{3} + 5 a^{2} - 6 a - 5\) , \( 4 a^{3} - 15 a^{2} + 9 a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-a^{3}+5a^{2}-6a-5\right){x}+4a^{3}-15a^{2}+9a+1$ |
| 4.1-c2 |
4.1-c |
$2$ |
$11$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{2} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.2 |
$14641$ |
\( 1 \) |
$1$ |
$0.020890025$ |
2.871111419 |
\( -58621608199599841261523685365125 a^{3} + \frac{186324765270697790904663848098547}{2} a^{2} + 238215298486610603874100648409004 a - \frac{397963624619871051990068501920911}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 3\) , \( a^{3} - 4 a - 3\) , \( 2901 a^{3} - 866 a^{2} - 14883 a - 8216\) , \( 10717520 a^{3} - 2961886 a^{2} - 55727837 a - 29617279\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(2901a^{3}-866a^{2}-14883a-8216\right){x}+10717520a^{3}-2961886a^{2}-55727837a-29617279$ |
| 4.1-d1 |
4.1-d |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{3} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$921.3779933$ |
0.480513580 |
\( \frac{5170795}{4} a^{3} - \frac{11305515}{4} a^{2} - \frac{18112897}{4} a + \frac{32436575}{4} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a^{3} - a^{2} - 3 a - 1\) , \( a^{3} - 4 a - 2\) , \( -3 a^{3} + 8 a^{2} + a - 5\) , \( 75 a^{3} - 210 a^{2} - 4 a + 87\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a-1\right){x}^{2}+\left(-3a^{3}+8a^{2}+a-5\right){x}+75a^{3}-210a^{2}-4a+87$ |
| 4.1-d2 |
4.1-d |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.37503695$ |
0.480513580 |
\( -\frac{13274440865651}{8} a^{3} + \frac{36869954817925}{8} a^{2} + \frac{895143848177}{8} a - \frac{14988334856695}{8} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 5 a + 4\) , \( 1\) , \( 130 a^{3} - 45 a^{2} - 668 a - 318\) , \( 2334 a^{3} - 636 a^{2} - 12144 a - 6492\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a+4\right){x}^{2}+\left(130a^{3}-45a^{2}-668a-318\right){x}+2334a^{3}-636a^{2}-12144a-6492$ |
| 4.1-d3 |
4.1-d |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{3} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$921.3779933$ |
0.480513580 |
\( -\frac{4921}{2} a^{3} + 6772 a^{2} + 1016 a - \frac{9321}{2} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 5 a + 4\) , \( 1\) , \( -15 a^{3} + 5 a^{2} + 77 a + 37\) , \( -17 a^{3} + 4 a^{2} + 89 a + 50\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a+4\right){x}^{2}+\left(-15a^{3}+5a^{2}+77a+37\right){x}-17a^{3}+4a^{2}+89a+50$ |
| 4.1-d4 |
4.1-d |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.37503695$ |
0.480513580 |
\( -\frac{576237781537807354959}{64} a^{3} + \frac{159190226393205886841}{64} a^{2} + \frac{2996401580039519157509}{64} a + \frac{1592384258224686624515}{64} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - 4 a - 3\) , \( -20 a^{3} - 73 a^{2} + 20 a + 26\) , \( -312 a^{3} - 648 a^{2} + 235 a + 280\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(-20a^{3}-73a^{2}+20a+26\right){x}-312a^{3}-648a^{2}+235a+280$ |
| 8.1-a1 |
8.1-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{5} \) |
$12.34481$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$989.9313991$ |
2.323193825 |
\( -\frac{10546970661}{2} a^{3} + \frac{29270065195}{2} a^{2} + \frac{761086087}{2} a - \frac{11870894695}{2} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a + 1\) , \( 2 a^{3} - 5 a^{2} - a + 10\) , \( -2 a^{3} + 7 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-1\right){x}^{2}+\left(2a^{3}-5a^{2}-a+10\right){x}-2a^{3}+7a^{2}+3a-5$ |
| 8.1-a2 |
8.1-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{5} \) |
$12.34481$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$989.9313991$ |
2.323193825 |
\( \frac{2414701}{2} a^{3} - \frac{3753195}{2} a^{2} - \frac{9723023}{2} a + \frac{8089111}{2} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 3\) , \( a^{3} - 4 a - 3\) , \( -a^{3} + 2 a^{2} + 2 a - 7\) , \( a^{2} - 2 a - 7\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{3}+2a^{2}+2a-7\right){x}+a^{2}-2a-7$ |
| 8.1-a3 |
8.1-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$12.34481$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1979.862798$ |
2.323193825 |
\( -\frac{79783}{4} a^{3} + \frac{220257}{4} a^{2} + \frac{6221}{4} a - \frac{76005}{4} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 6 a + 2\) , \( 0\) , \( -a^{3} - 2 a^{2} + 11 a + 7\) , \( -4 a^{3} + 9 a^{2} + 5 a - 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-a^{3}-2a^{2}+11a+7\right){x}-4a^{3}+9a^{2}+5a-1$ |
| 8.1-a4 |
8.1-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{16} \) |
$12.34481$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$123.7414248$ |
2.323193825 |
\( -\frac{21813780719}{256} a^{3} + \frac{6026311257}{256} a^{2} + \frac{113430164197}{256} a + \frac{60280404931}{256} \) |
\( \bigl[a + 1\) , \( -1\) , \( a^{3} - 4 a - 3\) , \( -a^{3} + 2 a^{2} - a - 1\) , \( 2 a^{3} - 2 a^{2} - 10 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}-{x}^{2}+\left(-a^{3}+2a^{2}-a-1\right){x}+2a^{3}-2a^{2}-10a-5$ |
| 8.1-a5 |
8.1-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$12.34481$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$123.7414248$ |
2.323193825 |
\( \frac{8273723503}{4} a^{3} + \frac{12005277671}{4} a^{2} - \frac{7160398413}{4} a - \frac{4242666811}{4} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( a^{3} - 5 a - 2\) , \( -438 a^{3} + 693 a^{2} + 1778 a - 1479\) , \( 7385 a^{3} - 11737 a^{2} - 30013 a + 25063\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+2\right){x}^{2}+\left(-438a^{3}+693a^{2}+1778a-1479\right){x}+7385a^{3}-11737a^{2}-30013a+25063$ |
| 8.1-a6 |
8.1-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(a), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$989.9313991$ |
2.323193825 |
\( \frac{153601}{16} a^{3} + \frac{115977}{16} a^{2} - \frac{103403}{16} a + \frac{338387}{16} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( a^{3} - 5 a - 2\) , \( -28 a^{3} + 43 a^{2} + 113 a - 89\) , \( 90 a^{3} - 142 a^{2} - 367 a + 299\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+2\right){x}^{2}+\left(-28a^{3}+43a^{2}+113a-89\right){x}+90a^{3}-142a^{2}-367a+299$ |
| 8.1-b1 |
8.1-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{16} \) |
$12.34481$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.135663182$ |
$244.9061432$ |
1.871342443 |
\( -\frac{21813780719}{256} a^{3} + \frac{6026311257}{256} a^{2} + \frac{113430164197}{256} a + \frac{60280404931}{256} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{2} - 3\) , \( a^{2} - a - 2\) , \( -12 a^{3} + 37 a^{2} + a - 13\) , \( -4 a^{3} + 15 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-12a^{3}+37a^{2}+a-13\right){x}-4a^{3}+15a^{2}+3a-5$ |
| 8.1-b2 |
8.1-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$12.34481$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.033915795$ |
$979.6245730$ |
1.871342443 |
\( \frac{8273723503}{4} a^{3} + \frac{12005277671}{4} a^{2} - \frac{7160398413}{4} a - \frac{4242666811}{4} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{2} - 3\) , \( -34 a^{3} + 45 a^{2} + 136 a - 87\) , \( 164 a^{3} - 264 a^{2} - 660 a + 580\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(-34a^{3}+45a^{2}+136a-87\right){x}+164a^{3}-264a^{2}-660a+580$ |
| 8.1-b3 |
8.1-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.067831591$ |
$1959.249146$ |
1.871342443 |
\( \frac{153601}{16} a^{3} + \frac{115977}{16} a^{2} - \frac{103403}{16} a + \frac{338387}{16} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{2} - 3\) , \( -4 a^{3} + 5 a^{2} + 21 a + 3\) , \( a^{3} - 3 a^{2} + 2 a + 20\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(-4a^{3}+5a^{2}+21a+3\right){x}+a^{3}-3a^{2}+2a+20$ |
| 8.1-b4 |
8.1-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$12.34481$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.135663182$ |
$979.6245730$ |
1.871342443 |
\( -\frac{79783}{4} a^{3} + \frac{220257}{4} a^{2} + \frac{6221}{4} a - \frac{76005}{4} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 0\) , \( 34 a^{3} - 9 a^{2} - 172 a - 86\) , \( -120 a^{3} + 34 a^{2} + 628 a + 336\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(34a^{3}-9a^{2}-172a-86\right){x}-120a^{3}+34a^{2}+628a+336$ |
| 8.1-b5 |
8.1-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{5} \) |
$12.34481$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.271326365$ |
$244.9061432$ |
1.871342443 |
\( \frac{2414701}{2} a^{3} - \frac{3753195}{2} a^{2} - \frac{9723023}{2} a + \frac{8089111}{2} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -19 a^{3} + 27 a^{2} + 79 a - 51\) , \( -98 a^{3} + 154 a^{2} + 399 a - 326\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-19a^{3}+27a^{2}+79a-51\right){x}-98a^{3}+154a^{2}+399a-326$ |
| 8.1-b6 |
8.1-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{5} \) |
$12.34481$ |
$(a), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.271326365$ |
$244.9061432$ |
1.871342443 |
\( -\frac{10546970661}{2} a^{3} + \frac{29270065195}{2} a^{2} + \frac{761086087}{2} a - \frac{11870894695}{2} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a^{3} - 5 a - 2\) , \( 2 a^{3} + 4 a^{2} + a\) , \( -2 a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{3}+4a^{2}+a\right){x}-2a^{2}-4a-2$ |
| 8.2-a1 |
8.2-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$12.34481$ |
$(-a-1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3007.493564$ |
0.882256902 |
\( -32793 a^{3} + 91679 a^{2} + 7795 a - 33051 \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 4 a\) , \( 103 a^{3} - 164 a^{2} - 420 a + 352\) , \( 893 a^{3} - 1419 a^{2} - 3629 a + 3031\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(103a^{3}-164a^{2}-420a+352\right){x}+893a^{3}-1419a^{2}-3629a+3031$ |
| 8.2-a2 |
8.2-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1503.746782$ |
0.882256902 |
\( -623 a^{3} - 71 a^{2} + 3845 a + 5315 \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( 0\) , \( 4 a^{3} - 2 a^{2} - 18 a + 3\) , \( 7 a^{3} - 4 a^{2} - 32 a - 8\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+4\right){x}^{2}+\left(4a^{3}-2a^{2}-18a+3\right){x}+7a^{3}-4a^{2}-32a-8$ |
| 8.2-a3 |
8.2-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$12.34481$ |
$(-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$751.8733911$ |
0.882256902 |
\( 1068917 a^{3} - 1698543 a^{2} - 4344039 a + 3628683 \) |
\( \bigl[a + 1\) , \( a^{3} - 5 a - 4\) , \( a^{3} - a^{2} - 4 a\) , \( -6 a^{3} + 4 a^{2} + 28 a + 14\) , \( 19 a^{3} - 5 a^{2} - 98 a - 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-5a-4\right){x}^{2}+\left(-6a^{3}+4a^{2}+28a+14\right){x}+19a^{3}-5a^{2}-98a-53$ |
| 8.2-a4 |
8.2-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$11.74802173$ |
0.882256902 |
\( -393049013796927 a^{3} + 108582701432571 a^{2} + 2043831237525567 a + 1086158495384435 \) |
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( a^{3} - 5 a - 2\) , \( 15 a^{3} + 52 a^{2} - 128 a - 307\) , \( 228 a^{3} + 337 a^{2} - 1532 a - 2508\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(15a^{3}+52a^{2}-128a-307\right){x}+228a^{3}+337a^{2}-1532a-2508$ |
| 8.2-a5 |
8.2-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$12.34481$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$187.9683477$ |
0.882256902 |
\( -7651323 a^{3} + 2646009 a^{2} + 40902633 a + 21644051 \) |
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( a^{3} - 5 a - 2\) , \( 2 a^{2} - 3 a - 12\) , \( 6 a^{3} + 7 a^{2} - 39 a - 59\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(2a^{2}-3a-12\right){x}+6a^{3}+7a^{2}-39a-59$ |
| 8.2-a6 |
8.2-a |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$11.74802173$ |
0.882256902 |
\( 1871271216191 a^{3} + 3084029329157 a^{2} - 1246733719103 a - 1422504331683 \) |
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( a^{3} - 5 a - 2\) , \( 5 a^{3} - 8 a^{2} - 18 a + 3\) , \( 4 a^{3} + 7 a^{2} - 20 a - 74\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(5a^{3}-8a^{2}-18a+3\right){x}+4a^{3}+7a^{2}-20a-74$ |
| 8.2-b1 |
8.2-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$12.34481$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.172750202$ |
$915.7167659$ |
2.969956322 |
\( 1068917 a^{3} - 1698543 a^{2} - 4344039 a + 3628683 \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{2} - 4\) , \( a + 1\) , \( -11 a^{3} + 30 a^{2} + 6 a - 5\) , \( 7 a^{3} - 17 a^{2} + 2 a + 7\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-11a^{3}+30a^{2}+6a-5\right){x}+7a^{3}-17a^{2}+2a+7$ |
| 8.2-b2 |
8.2-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.382001617$ |
$57.23229787$ |
2.969956322 |
\( -393049013796927 a^{3} + 108582701432571 a^{2} + 2043831237525567 a + 1086158495384435 \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -654 a^{3} + 1043 a^{2} + 2660 a - 2235\) , \( -14751 a^{3} + 23453 a^{2} + 59929 a - 50085\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(-654a^{3}+1043a^{2}+2660a-2235\right){x}-14751a^{3}+23453a^{2}+59929a-50085$ |
| 8.2-b3 |
8.2-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$12.34481$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.691000808$ |
$915.7167659$ |
2.969956322 |
\( -7651323 a^{3} + 2646009 a^{2} + 40902633 a + 21644051 \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -39 a^{3} + 63 a^{2} + 165 a - 140\) , \( -236 a^{3} + 379 a^{2} + 958 a - 803\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(-39a^{3}+63a^{2}+165a-140\right){x}-236a^{3}+379a^{2}+958a-803$ |
| 8.2-b4 |
8.2-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.382001617$ |
$228.9291914$ |
2.969956322 |
\( 1871271216191 a^{3} + 3084029329157 a^{2} - 1246733719103 a - 1422504331683 \) |
\( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a + 1\) , \( 137 a^{3} - 39 a^{2} - 713 a - 378\) , \( 2176 a^{3} - 601 a^{2} - 11316 a - 6015\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(137a^{3}-39a^{2}-713a-378\right){x}+2176a^{3}-601a^{2}-11316a-6015$ |
| 8.2-b5 |
8.2-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$12.34481$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.172750202$ |
$915.7167659$ |
2.969956322 |
\( -32793 a^{3} + 91679 a^{2} + 7795 a - 33051 \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 5 a\) , \( a + 1\) , \( 5 a^{3} - 11 a^{2} - 19 a + 29\) , \( 12 a^{3} - 23 a^{2} - 51 a + 49\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(5a^{3}-11a^{2}-19a+29\right){x}+12a^{3}-23a^{2}-51a+49$ |
| 8.2-b6 |
8.2-b |
$6$ |
$8$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.345500404$ |
$1831.433531$ |
2.969956322 |
\( -623 a^{3} - 71 a^{2} + 3845 a + 5315 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -2 a^{2} + 6\) , \( -a^{2} + 3\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-2a^{2}+6\right){x}-a^{2}+3$ |
| 8.3-a1 |
8.3-a |
$1$ |
$1$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$12.34481$ |
$(a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$148.7727753$ |
2.793147027 |
\( \frac{20757}{2} a^{3} - \frac{58115}{2} a^{2} + 154 a + 12302 \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - a^{2} - 4 a\) , \( -19 a^{3} + 3 a^{2} + 101 a + 62\) , \( -61 a^{3} + 16 a^{2} + 318 a + 172\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(-19a^{3}+3a^{2}+101a+62\right){x}-61a^{3}+16a^{2}+318a+172$ |
| 8.3-b1 |
8.3-b |
$1$ |
$1$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{10} \) |
$12.34481$ |
$(a), (-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.011372231$ |
$653.0953744$ |
1.673300328 |
\( \frac{20757}{2} a^{3} - \frac{58115}{2} a^{2} + 154 a + 12302 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( -a^{3} + 7 a + 5\) , \( a^{3} - 5 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-a^{3}+7a+5\right){x}+a^{3}-5a-3$ |
| 8.4-a1 |
8.4-a |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$12.34481$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$693.6737859$ |
3.255859260 |
\( 89104 a^{3} - 140304 a^{2} - 365648 a + 304864 \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{3} - 4 a - 2\) , \( -3 a^{3} + 11 a + 3\) , \( -2 a^{3} + 8 a + 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(-3a^{3}+11a+3\right){x}-2a^{3}+8a+3$ |
| 8.4-a2 |
8.4-a |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$693.6737859$ |
3.255859260 |
\( -368 a^{3} - 240 a^{2} + 2512 a + 3248 \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -4 a^{3} + 7 a^{2} + 16 a - 15\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-4a^{3}+7a^{2}+16a-15\right){x}-1$ |
| 8.4-b1 |
8.4-b |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{8} \) |
$12.34481$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$260.4035341$ |
1.222242032 |
\( 262208 a^{3} + 1023968 a^{2} - 262464 a - 445808 \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + 4 a + 2\) , \( a^{2} - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 65 a^{3} - 20 a^{2} - 337 a - 179\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(a^{3}-a^{2}-2a+1\right){x}+65a^{3}-20a^{2}-337a-179$ |
| 8.4-b2 |
8.4-b |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{4} \) |
$12.34481$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$260.4035341$ |
1.222242032 |
\( -14336 a^{3} + 2048 a^{2} + 75776 a + 47104 \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( 2 a^{3} - 4 a^{2} - 3 a + 4\) , \( 5 a^{3} - 14 a^{2} + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(2a^{3}-4a^{2}-3a+4\right){x}+5a^{3}-14a^{2}+4$ |
| 8.4-c1 |
8.4-c |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{8} \) |
$12.34481$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.034941082$ |
$1537.735206$ |
2.017521841 |
\( 262208 a^{3} + 1023968 a^{2} - 262464 a - 445808 \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( a\) , \( 5 a^{3} - 14 a^{2} - a + 7\) , \( -25 a^{3} + 70 a^{2} - 29\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(5a^{3}-14a^{2}-a+7\right){x}-25a^{3}+70a^{2}-29$ |
| 8.4-c2 |
8.4-c |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{4} \) |
$12.34481$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.069882165$ |
$1537.735206$ |
2.017521841 |
\( -14336 a^{3} + 2048 a^{2} + 75776 a + 47104 \) |
\( \bigl[0\) , \( a^{3} - 6 a - 2\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{3}-6a-2\right){x}^{2}-a{x}$ |
| 8.4-d1 |
8.4-d |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$12.34481$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.070674530$ |
$925.5227000$ |
1.228062135 |
\( 89104 a^{3} - 140304 a^{2} - 365648 a + 304864 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 3 a + 1\) , \( a\) , \( -7 a^{3} - 3 a^{2} + 10 a + 5\) , \( -7 a^{3} - 7 a^{2} + 7 a + 5\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+3a+1\right){x}^{2}+\left(-7a^{3}-3a^{2}+10a+5\right){x}-7a^{3}-7a^{2}+7a+5$ |
| 8.4-d2 |
8.4-d |
$2$ |
$2$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$12.34481$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.035337265$ |
$925.5227000$ |
1.228062135 |
\( -368 a^{3} - 240 a^{2} + 2512 a + 3248 \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( -64 a^{3} + 103 a^{2} + 256 a - 215\) , \( -11 a^{3} + 18 a^{2} + 42 a - 37\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(-64a^{3}+103a^{2}+256a-215\right){x}-11a^{3}+18a^{2}+42a-37$ |
| 14.1-a1 |
14.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{30} \cdot 7^{6} \) |
$13.23928$ |
$(a), (a^3-a^2-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.078912103$ |
$7.599853298$ |
1.779766055 |
\( -\frac{4344977037336450055}{126324651851776} a^{3} - \frac{20805037680357238655}{126324651851776} a^{2} - \frac{4483998603304559635}{126324651851776} a + \frac{16007017427212152571}{126324651851776} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 6 a - 2\) , \( a^{2} - a - 3\) , \( -123 a^{3} + 188 a^{2} + 509 a - 379\) , \( -1145 a^{3} + 1812 a^{2} + 4665 a - 3856\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-6a-2\right){x}^{2}+\left(-123a^{3}+188a^{2}+509a-379\right){x}-1145a^{3}+1812a^{2}+4665a-3856$ |
| 14.1-a2 |
14.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{10} \cdot 7^{2} \) |
$13.23928$ |
$(a), (a^3-a^2-4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.692970701$ |
$615.5881171$ |
1.779766055 |
\( \frac{421428745}{50176} a^{3} - \frac{514332911}{50176} a^{2} - \frac{1855299779}{50176} a + \frac{726482475}{50176} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 6 a - 2\) , \( a^{2} - a - 3\) , \( -8 a^{3} + 18 a^{2} + 29 a - 44\) , \( 23 a^{3} - 36 a^{2} - 92 a + 80\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-6a-2\right){x}^{2}+\left(-8a^{3}+18a^{2}+29a-44\right){x}+23a^{3}-36a^{2}-92a+80$ |
| 14.1-a3 |
14.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{5} \cdot 7 \) |
$13.23928$ |
$(a), (a^3-a^2-4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1.385941402$ |
$1231.176234$ |
1.779766055 |
\( -\frac{8223137845}{224} a^{3} + \frac{2272095331}{224} a^{2} + \frac{42760080679}{224} a + \frac{22723964561}{224} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 5 a - 3\) , \( 5 a^{3} - 3 a^{2} - 26 a - 7\) , \( -7 a^{3} - a^{2} + 27 a + 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-5a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(5a^{3}-3a^{2}-26a-7\right){x}-7a^{3}-a^{2}+27a+12$ |
| 14.1-a4 |
14.1-a |
$4$ |
$6$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{15} \cdot 7^{3} \) |
$13.23928$ |
$(a), (a^3-a^2-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$4.157824207$ |
$15.19970659$ |
1.779766055 |
\( \frac{1242409545080523731}{11239424} a^{3} + \frac{2110913976994909867}{11239424} a^{2} - \frac{836271356526981681}{11239424} a - \frac{971452564716753111}{11239424} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 5 a - 3\) , \( -40 a^{3} - 88 a^{2} - a + 28\) , \( -800 a^{3} - 1336 a^{2} + 534 a + 612\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-5a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(-40a^{3}-88a^{2}-a+28\right){x}-800a^{3}-1336a^{2}+534a+612$ |
*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.
