| 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 |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$3.73146$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$147.6626516$ |
3.969196667 |
\( -\frac{275633451}{2} a^{2} - \frac{143162239}{2} a + 1268850167 \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - 2 a + 7\) , \( a^{2} + a - 7\) , \( -204 a^{2} - 366 a + 1027\) , \( 5813 a^{2} + 10379 a - 29215\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(-204a^{2}-366a+1027\right){x}+5813a^{2}+10379a-29215$ |
| 2.1-b1 |
2.1-b |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$3.73146$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.140734634$ |
$213.7884014$ |
2.426265595 |
\( -\frac{275633451}{2} a^{2} - \frac{143162239}{2} a + 1268850167 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a^{2} + 2 a - 6\) , \( -25 a^{2} - 51 a + 103\) , \( -439 a^{2} - 775 a + 2235\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-25a^{2}-51a+103\right){x}-439a^{2}-775a+2235$ |
| 4.1-a1 |
4.1-a |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$60.12549720$ |
1.212137533 |
\( 12303 a^{2} - 51716 a + 50262 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -1\) , \( a^{2} + 2 a - 6\) , \( 3 a^{2} + 6 a - 15\) , \( 8 a^{2} + 14 a - 42\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}-{x}^{2}+\left(3a^{2}+6a-15\right){x}+8a^{2}+14a-42$ |
| 4.1-a2 |
4.1-a |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$60.12549720$ |
1.212137533 |
\( -28409855 a^{2} - 14729216 a + 262030078 \) |
\( \bigl[a\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 6\) , \( 55563 a^{2} + 28909 a - 511678\) , \( 12455823 a^{2} + 6479902 a - 114707281\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+2a-6\right){x}^{2}+\left(55563a^{2}+28909a-511678\right){x}+12455823a^{2}+6479902a-114707281$ |
| 4.1-a3 |
4.1-a |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 3 \) |
$1$ |
$240.5019888$ |
1.212137533 |
\( -1993 a^{2} - 1028 a + 20118 \) |
\( \bigl[a\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 6\) , \( 3538 a^{2} + 1844 a - 32573\) , \( 187106 a^{2} + 97341 a - 1723075\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+2a-6\right){x}^{2}+\left(3538a^{2}+1844a-32573\right){x}+187106a^{2}+97341a-1723075$ |
| 4.1-a4 |
4.1-a |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$240.5019888$ |
1.212137533 |
\( 19719 a^{2} + 35872 a - 95198 \) |
\( \bigl[a\) , \( -a^{2} - a + 8\) , \( 0\) , \( 740615 a^{2} + 385290 a - 6820418\) , \( -486835272 a^{2} - 253266566 a + 4483329158\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}-a+8\right){x}^{2}+\left(740615a^{2}+385290a-6820418\right){x}-486835272a^{2}-253266566a+4483329158$ |
| 4.1-b1 |
4.1-b |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$95.35661317$ |
0.640800410 |
\( 12303 a^{2} - 51716 a + 50262 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a - 1\) , \( 0\) , \( 2 a^{2} + 16 a - 27\) , \( -3 a^{2} + 45 a - 62\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{2}+16a-27\right){x}-3a^{2}+45a-62$ |
| 4.1-b2 |
4.1-b |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$95.35661317$ |
0.640800410 |
\( 19719 a^{2} + 35872 a - 95198 \) |
\( \bigl[a\) , \( a^{2} + 2 a - 6\) , \( a\) , \( 1216 a^{2} + 636 a - 11183\) , \( 32300 a^{2} + 16808 a - 297440\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+2a-6\right){x}^{2}+\left(1216a^{2}+636a-11183\right){x}+32300a^{2}+16808a-297440$ |
| 4.1-b3 |
4.1-b |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$381.4264526$ |
0.640800410 |
\( -28409855 a^{2} - 14729216 a + 262030078 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 91 a^{2} + 47 a - 836\) , \( -884 a^{2} - 460 a + 8141\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(91a^{2}+47a-836\right){x}-884a^{2}-460a+8141$ |
| 4.1-b4 |
4.1-b |
$4$ |
$4$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$4.18842$ |
$(a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$381.4264526$ |
0.640800410 |
\( -1993 a^{2} - 1028 a + 20118 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 6 a^{2} + 2 a - 51\) , \( -16 a^{2} - 9 a + 149\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a^{2}+2a-51\right){x}-16a^{2}-9a+149$ |
| 4.2-a1 |
4.2-a |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$4.18842$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$72.74235068$ |
1.955326500 |
\( \frac{74263}{32} a^{2} - \frac{81357}{8} a + \frac{161647}{16} \) |
\( \bigl[a^{2} + a - 7\) , \( a + 1\) , \( 1\) , \( 2 a + 7\) , \( a + 3\bigr] \) |
${y}^2+\left(a^{2}+a-7\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+7\right){x}+a+3$ |
| 4.2-a2 |
4.2-a |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{12} \) |
$4.18842$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$72.74235068$ |
1.955326500 |
\( \frac{66014871}{1024} a^{2} + \frac{31019783}{256} a - \frac{155640621}{512} \) |
\( \bigl[a^{2} + a - 7\) , \( -a^{2} - a + 6\) , \( a^{2} + 2 a - 6\) , \( 8 a^{2} + 2 a - 80\) , \( -18 a^{2} - 10 a + 154\bigr] \) |
${y}^2+\left(a^{2}+a-7\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(8a^{2}+2a-80\right){x}-18a^{2}-10a+154$ |
| 4.2-b1 |
4.2-b |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{12} \) |
$4.18842$ |
$(a-2), (a^2+2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.158632240$ |
$93.52368836$ |
1.196372145 |
\( \frac{66014871}{1024} a^{2} + \frac{31019783}{256} a - \frac{155640621}{512} \) |
\( \bigl[1\) , \( a^{2} + a - 7\) , \( a^{2} + a - 6\) , \( 6475 a^{2} + 3369 a - 59628\) , \( 474452 a^{2} + 246824 a - 4369292\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(6475a^{2}+3369a-59628\right){x}+474452a^{2}+246824a-4369292$ |
| 4.2-b2 |
4.2-b |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$4.18842$ |
$(a-2), (a^2+2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.317264480$ |
$93.52368836$ |
1.196372145 |
\( \frac{74263}{32} a^{2} - \frac{81357}{8} a + \frac{161647}{16} \) |
\( \bigl[1\) , \( -a^{2} - 2 a + 6\) , \( a + 1\) , \( 2 a + 9\) , \( 47 a^{2} + 22 a - 442\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(2a+9\right){x}+47a^{2}+22a-442$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$76.27756935$ |
1.537765325 |
\( -\frac{176450177611641}{8} a^{2} - \frac{22948692406921}{2} a + \frac{812476288285571}{4} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( 1\) , \( 0\) , \( -4270 a^{2} + 18442 a - 18169\) , \( -586349 a^{2} + 2524846 a - 2483236\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}={x}^{3}+{x}^{2}+\left(-4270a^{2}+18442a-18169\right){x}-586349a^{2}+2524846a-2483236$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$228.8327080$ |
1.537765325 |
\( -\frac{8185}{2} a^{2} + 2542 a + 57603 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( 1\) , \( 0\) , \( -155 a^{2} + 722 a - 739\) , \( 3354 a^{2} - 14354 a + 14070\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}={x}^{3}+{x}^{2}+\left(-155a^{2}+722a-739\right){x}+3354a^{2}-14354a+14070$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$38.13878467$ |
1.537765325 |
\( \frac{7406183446791}{64} a^{2} - \frac{7972420015113}{16} a + \frac{15681242700803}{32} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -50 a^{2} + 1889 a - 4878\) , \( -23608 a^{2} + 71978 a - 17312\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-50a^{2}+1889a-4878\right){x}-23608a^{2}+71978a-17312$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$114.4163540$ |
1.537765325 |
\( \frac{2151}{4} a^{2} - 2313 a + \frac{4547}{2} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5 a^{2} + 19 a - 18\) , \( -58 a^{2} + 130 a + 86\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a^{2}+19a-18\right){x}-58a^{2}+130a+86$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$95.37181135$ |
0.640902542 |
\( -\frac{255705709529849}{524288} a^{2} - \frac{8937357483529}{131072} a + \frac{1338228125264387}{262144} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( a^{2} - 7\) , \( a^{2} + 2 a - 6\) , \( -801 a^{2} + 3478 a - 3435\) , \( 46006 a^{2} - 198040 a + 194752\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(-801a^{2}+3478a-3435\right){x}+46006a^{2}-198040a+194752$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{42} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$47.68590567$ |
0.640902542 |
\( \frac{1614503812744071}{274877906944} a^{2} - \frac{183789830530953}{68719476736} a - \frac{9759532008734077}{137438953472} \) |
\( \bigl[a\) , \( -a^{2} - 2 a + 7\) , \( a^{2} + 2 a - 6\) , \( 1124 a^{2} + 625 a - 10467\) , \( -35994 a^{2} - 18554 a + 330980\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(1124a^{2}+625a-10467\right){x}-35994a^{2}-18554a+330980$ |
| 8.1-c1 |
8.1-c |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$9$ |
\( 3 \) |
$1$ |
$8.181078828$ |
1.484384138 |
\( -\frac{255705709529849}{524288} a^{2} - \frac{8937357483529}{131072} a + \frac{1338228125264387}{262144} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( a\) , \( 0\) , \( 565 a^{2} + 350 a - 5272\) , \( 13074 a^{2} + 6534 a - 119499\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}={x}^{3}+a{x}^{2}+\left(565a^{2}+350a-5272\right){x}+13074a^{2}+6534a-119499$ |
| 8.1-c2 |
8.1-c |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{42} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$4.090539414$ |
1.484384138 |
\( \frac{1614503812744071}{274877906944} a^{2} - \frac{183789830530953}{68719476736} a - \frac{9759532008734077}{137438953472} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 692271 a^{2} + 360139 a - 6375209\) , \( 555301191 a^{2} + 288884626 a - 5113840684\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(692271a^{2}+360139a-6375209\right){x}+555301191a^{2}+288884626a-5113840684$ |
| 8.1-d1 |
8.1-d |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$8.111332148$ |
0.490576407 |
\( -\frac{176450177611641}{8} a^{2} - \frac{22948692406921}{2} a + \frac{812476288285571}{4} \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a^{2} - 2 a + 7\) , \( a^{2} + 2 a - 6\) , \( 124 a^{2} + 286 a - 1769\) , \( 1530 a^{2} + 4222 a - 23634\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(124a^{2}+286a-1769\right){x}+1530a^{2}+4222a-23634$ |
| 8.1-d2 |
8.1-d |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$219.0059680$ |
0.490576407 |
\( -\frac{8185}{2} a^{2} + 2542 a + 57603 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( -a^{2} - 2 a + 7\) , \( a^{2} + 2 a - 6\) , \( -a^{2} + 6 a - 19\) , \( 6 a^{2} - 6 a - 30\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(-a^{2}+6a-19\right){x}+6a^{2}-6a-30$ |
| 8.1-d3 |
8.1-d |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$4.055666074$ |
0.490576407 |
\( \frac{7406183446791}{64} a^{2} - \frac{7972420015113}{16} a + \frac{15681242700803}{32} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 212107 a^{2} + 110365 a - 1953375\) , \( 93039091 a^{2} + 48401890 a - 856809376\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(212107a^{2}+110365a-1953375\right){x}+93039091a^{2}+48401890a-856809376$ |
| 8.1-d4 |
8.1-d |
$4$ |
$6$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$109.5029840$ |
0.490576407 |
\( \frac{2151}{4} a^{2} - 2313 a + \frac{4547}{2} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -48 a^{2} - 25 a + 445\) , \( 371158 a^{2} + 193088 a - 3418042\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-48a^{2}-25a+445\right){x}+371158a^{2}+193088a-3418042$ |
| 8.2-a1 |
8.2-a |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$4.70134$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$196.9248166$ |
2.646685933 |
\( 6935 a^{2} + 3100 a - 62298 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( a - 1\) , \( a^{2} + 2 a - 6\) , \( 8 a^{2} + 12 a - 45\) , \( 14 a^{2} + 27 a - 66\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a^{2}+12a-45\right){x}+14a^{2}+27a-66$ |
| 8.2-a2 |
8.2-a |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$4.70134$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$196.9248166$ |
2.646685933 |
\( -292941831 a^{2} - 152395772 a + 2697745162 \) |
\( \bigl[a\) , \( a^{2} + a - 6\) , \( a\) , \( 408 a^{2} + 213 a - 3754\) , \( -8033 a^{2} - 4180 a + 73974\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(408a^{2}+213a-3754\right){x}-8033a^{2}-4180a+73974$ |
| 8.2-b1 |
8.2-b |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{11} \) |
$4.70134$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.136190188$ |
$135.5242003$ |
1.488387051 |
\( -2431573 a^{2} - 4336493 a + 12238126 \) |
\( \bigl[a^{2} + a - 6\) , \( a\) , \( a^{2} + 2 a - 6\) , \( -7 a^{2} - 17 a + 24\) , \( 7 a^{2} + 16 a - 25\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+a{x}^{2}+\left(-7a^{2}-17a+24\right){x}+7a^{2}+16a-25$ |
| 8.2-c1 |
8.2-c |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$4.70134$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.424250889$ |
$84.44736610$ |
2.889096708 |
\( 6935 a^{2} + 3100 a - 62298 \) |
\( \bigl[a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 7\) , \( a^{2} + 2 a - 6\) , \( 13 a^{2} + 26 a - 69\) , \( 37 a^{2} + 62 a - 180\bigr] \) |
${y}^2+\left(a^{2}+2a-6\right){x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(a^{2}+2a-7\right){x}^{2}+\left(13a^{2}+26a-69\right){x}+37a^{2}+62a-180$ |
| 8.2-c2 |
8.2-c |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$4.70134$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.848501778$ |
$84.44736610$ |
2.889096708 |
\( -292941831 a^{2} - 152395772 a + 2697745162 \) |
\( \bigl[a\) , \( -a^{2} - a + 8\) , \( a^{2} + 2 a - 6\) , \( -6 a^{2} - 10 a + 33\) , \( 8 a^{2} + 13 a - 44\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+2a-6\right){y}={x}^{3}+\left(-a^{2}-a+8\right){x}^{2}+\left(-6a^{2}-10a+33\right){x}+8a^{2}+13a-44$ |
| 8.2-d1 |
8.2-d |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{11} \) |
$4.70134$ |
$(a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$15.75807166$ |
0.423579590 |
\( -2431573 a^{2} - 4336493 a + 12238126 \) |
\( \bigl[a^{2} + a - 6\) , \( -a^{2} - 2 a + 8\) , \( a\) , \( -72 a^{2} - 129 a + 369\) , \( -628 a^{2} - 1121 a + 3157\bigr] \) |
${y}^2+\left(a^{2}+a-6\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-2a+8\right){x}^{2}+\left(-72a^{2}-129a+369\right){x}-628a^{2}-1121a+3157$ |
| 8.3-a1 |
8.3-a |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{27} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$1$ |
$15.03048530$ |
1.212065844 |
\( -\frac{3777931411479}{1024} a^{2} - \frac{1965395248155}{1024} a + \frac{17395730227843}{512} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} + 6\) , \( a + 1\) , \( 13 a^{2} + 16 a - 46\) , \( 325 a^{2} + 533 a - 1560\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(13a^{2}+16a-46\right){x}+325a^{2}+533a-1560$ |
| 8.3-b1 |
8.3-b |
$2$ |
$3$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{6} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.036562612$ |
$220.7794297$ |
3.905712637 |
\( -15408 a^{2} - \frac{54531}{2} a + \frac{156463}{2} \) |
\( \bigl[a + 1\) , \( -a^{2} - 2 a + 6\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+3{x}+1$ |
| 8.3-b2 |
8.3-b |
$2$ |
$3$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{10} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.109687837$ |
$73.59314325$ |
3.905712637 |
\( -\frac{853203431977899}{4} a^{2} - \frac{3047074444651623}{8} a + \frac{8575933878425641}{8} \) |
\( \bigl[a + 1\) , \( -a^{2} - 2 a + 6\) , \( 0\) , \( -15 a^{2} - 30 a + 68\) , \( 99 a^{2} + 180 a - 486\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(-15a^{2}-30a+68\right){x}+99a^{2}+180a-486$ |
| 8.3-c1 |
8.3-c |
$2$ |
$3$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{6} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$69.85447310$ |
1.251799913 |
\( -15408 a^{2} - \frac{54531}{2} a + \frac{156463}{2} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 7\) , \( 9 a^{2} + 17 a - 48\) , \( 14 a^{2} + 23 a - 68\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}+2a-6\right){x}^{2}+\left(9a^{2}+17a-48\right){x}+14a^{2}+23a-68$ |
| 8.3-c2 |
8.3-c |
$2$ |
$3$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{10} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$2.587202707$ |
1.251799913 |
\( -\frac{853203431977899}{4} a^{2} - \frac{3047074444651623}{8} a + \frac{8575933878425641}{8} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + 2 a - 6\) , \( a^{2} + 2 a - 7\) , \( -106 a^{2} - 193 a + 537\) , \( -2020 a^{2} - 3547 a + 10060\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}+2a-6\right){x}^{2}+\left(-106a^{2}-193a+537\right){x}-2020a^{2}-3547a+10060$ |
| 8.3-d1 |
8.3-d |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{27} \) |
$4.70134$ |
$(a-2), (a^2+2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \cdot 19 \) |
$0.021378956$ |
$36.66275925$ |
3.602796392 |
\( -\frac{3777931411479}{1024} a^{2} - \frac{1965395248155}{1024} a + \frac{17395730227843}{512} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 7\) , \( a + 1\) , \( 7 a^{2} + 5 a - 62\) , \( -24 a^{2} - 34 a + 149\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(7a^{2}+5a-62\right){x}-24a^{2}-34a+149$ |
| 8.4-a1 |
8.4-a |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$4.70134$ |
$(a^2+2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.065059414$ |
$310.4305544$ |
3.257300425 |
\( 634 a^{2} + 589 a - 5803 \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + 2 a - 8\) , \( a + 1\) , \( -23 a^{2} + 149 a - 170\) , \( 672 a^{2} - 2789 a + 2685\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+2a-8\right){x}^{2}+\left(-23a^{2}+149a-170\right){x}+672a^{2}-2789a+2685$ |
| 8.4-b1 |
8.4-b |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$4.70134$ |
$(a^2+2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.121773979$ |
$92.76324437$ |
1.821854258 |
\( 634 a^{2} + 589 a - 5803 \) |
\( \bigl[a + 1\) , \( -1\) , \( a^{2} + 2 a - 7\) , \( -a^{2} - 2\) , \( a^{2} - 4 a - 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}-{x}^{2}+\left(-a^{2}-2\right){x}+a^{2}-4a-6$ |
| 11.3-a1 |
11.3-a |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
11.3 |
\( 11 \) |
\( - 11^{2} \) |
$4.95761$ |
$(a^2+a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$102.4796627$ |
1.377335200 |
\( \frac{4969983}{121} a^{2} + \frac{8909449}{121} a - \frac{24807043}{121} \) |
\( \bigl[a^{2} + a - 7\) , \( -a^{2} - 2 a + 6\) , \( 1\) , \( 25 a^{2} - 103 a + 97\) , \( -395 a^{2} + 1702 a - 1679\bigr] \) |
${y}^2+\left(a^{2}+a-7\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(25a^{2}-103a+97\right){x}-395a^{2}+1702a-1679$ |
| 11.3-a2 |
11.3-a |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
11.3 |
\( 11 \) |
\( -11 \) |
$4.95761$ |
$(a^2+a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$204.9593254$ |
1.377335200 |
\( \frac{1500}{11} a^{2} - \frac{5466}{11} a + \frac{22613}{11} \) |
\( \bigl[a^{2} + a - 7\) , \( -a^{2} - 2 a + 7\) , \( 0\) , \( -3 a^{2} + 11 a - 4\) , \( -10 a^{2} + 40 a - 35\bigr] \) |
${y}^2+\left(a^{2}+a-7\right){x}{y}={x}^{3}+\left(-a^{2}-2a+7\right){x}^{2}+\left(-3a^{2}+11a-4\right){x}-10a^{2}+40a-35$ |
| 11.3-b1 |
11.3-b |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
11.3 |
\( 11 \) |
\( - 11^{2} \) |
$4.95761$ |
$(a^2+a-9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.122560176$ |
$193.0042802$ |
0.953760938 |
\( \frac{4969983}{121} a^{2} + \frac{8909449}{121} a - \frac{24807043}{121} \) |
\( \bigl[1\) , \( a^{2} + a - 8\) , \( a^{2} + a - 6\) , \( 671 a^{2} + 348 a - 6176\) , \( 3328 a^{2} + 1733 a - 30657\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}+a-8\right){x}^{2}+\left(671a^{2}+348a-6176\right){x}+3328a^{2}+1733a-30657$ |
| 11.3-b2 |
11.3-b |
$2$ |
$2$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
11.3 |
\( 11 \) |
\( -11 \) |
$4.95761$ |
$(a^2+a-9)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.245120352$ |
$193.0042802$ |
0.953760938 |
\( \frac{1500}{11} a^{2} - \frac{5466}{11} a + \frac{22613}{11} \) |
\( \bigl[1\) , \( -a^{2} + 6\) , \( a\) , \( -3 a^{2} - 3 a + 31\) , \( -3 a^{2} - a + 24\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-3a^{2}-3a+31\right){x}-3a^{2}-a+24$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{17} \cdot 7^{10} \) |
$5.16093$ |
$(a-2), (-a^2-a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$10.48259815$ |
2.817739841 |
\( -\frac{788489359263649}{144627327488} a^{2} - \frac{284810235386417}{144627327488} a + \frac{3579577447349559}{72313663744} \) |
\( \bigl[a + 1\) , \( a^{2} - 8\) , \( 1\) , \( -60 a^{2} + 258 a - 250\) , \( -1268 a^{2} + 5463 a - 5376\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(-60a^{2}+258a-250\right){x}-1268a^{2}+5463a-5376$ |
| 14.1-b1 |
14.1-b |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{17} \cdot 7^{10} \) |
$5.16093$ |
$(a-2), (-a^2-a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 17 \) |
$1$ |
$6.506524617$ |
5.946479817 |
\( -\frac{788489359263649}{144627327488} a^{2} - \frac{284810235386417}{144627327488} a + \frac{3579577447349559}{72313663744} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a\) , \( a\) , \( 84 a^{2} + 55 a - 759\) , \( 721 a^{2} + 393 a - 6613\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(84a^{2}+55a-759\right){x}+721a^{2}+393a-6613$ |
| 14.1-c1 |
14.1-c |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{5} \) |
$5.16093$ |
$(a-2), (-a^2-a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.122764211$ |
$29.61502708$ |
2.681352456 |
\( -\frac{896382355}{33614} a^{2} + \frac{4063355185}{33614} a - \frac{2181610832}{16807} \) |
\( \bigl[1\) , \( a^{2} + a - 8\) , \( 1\) , \( 5 a^{2} + 7 a - 32\) , \( -190 a^{2} - 331 a + 982\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}+a-8\right){x}^{2}+\left(5a^{2}+7a-32\right){x}-190a^{2}-331a+982$ |
| 14.1-d1 |
14.1-d |
$1$ |
$1$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{5} \) |
$5.16093$ |
$(a-2), (-a^2-a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.780079928$ |
$17.15633163$ |
5.396184007 |
\( -\frac{896382355}{33614} a^{2} + \frac{4063355185}{33614} a - \frac{2181610832}{16807} \) |
\( \bigl[a^{2} + a - 7\) , \( -a^{2} - 2 a + 6\) , \( 0\) , \( 21 a^{2} + 38 a - 103\) , \( 3141 a^{2} + 5609 a - 15785\bigr] \) |
${y}^2+\left(a^{2}+a-7\right){x}{y}={x}^{3}+\left(-a^{2}-2a+6\right){x}^{2}+\left(21a^{2}+38a-103\right){x}+3141a^{2}+5609a-15785$ |
| 14.1-e1 |
14.1-e |
$6$ |
$8$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$5.16093$ |
$(a-2), (-a^2-a+7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$132.8569705$ |
0.892804373 |
\( -\frac{12607859}{196} a^{2} + \frac{776149}{49} a + \frac{148898779}{196} \) |
\( \bigl[a^{2} + a - 7\) , \( a^{2} + 2 a - 7\) , \( 0\) , \( -9219 a^{2} - 16464 a + 46328\) , \( 914904 a^{2} + 1633712 a - 4598064\bigr] \) |
${y}^2+\left(a^{2}+a-7\right){x}{y}={x}^{3}+\left(a^{2}+2a-7\right){x}^{2}+\left(-9219a^{2}-16464a+46328\right){x}+914904a^{2}+1633712a-4598064$ |
| 14.1-e2 |
14.1-e |
$6$ |
$8$ |
3.3.1384.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{8} \) |
$5.16093$ |
$(a-2), (-a^2-a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.60712132$ |
0.892804373 |
\( \frac{59320144946578338229}{11529602} a^{2} - \frac{255426469572162371659}{11529602} a + \frac{125606139819660990618}{5764801} \) |
\( \bigl[a^{2} + a - 7\) , \( a^{2} + 2 a - 7\) , \( 0\) , \( -147334 a^{2} - 263109 a + 740398\) , \( 60153157 a^{2} + 107413573 a - 302313090\bigr] \) |
${y}^2+\left(a^{2}+a-7\right){x}{y}={x}^{3}+\left(a^{2}+2a-7\right){x}^{2}+\left(-147334a^{2}-263109a+740398\right){x}+60153157a^{2}+107413573a-302313090$ |
*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.
