| 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 |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$12.49752$ |
$(-2a^2+3a+8)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1333.894629$ |
1.300094701 |
\( -229125 a^{3} - \frac{83153}{2} a^{2} + 1510546 a + \frac{2938759}{2} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 5 a - 4\) , \( 34 a^{3} - 106 a^{2} - 19 a + 185\) , \( -177 a^{3} + 736 a^{2} - 103 a - 1447\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(34a^{3}-106a^{2}-19a+185\right){x}-177a^{3}+736a^{2}-103a-1447$ |
| 2.1-a2 |
2.1-a |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$12.49752$ |
$(-2a^2+3a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$666.9473147$ |
1.300094701 |
\( -\frac{1000078311417}{2} a^{3} - 91991441416 a^{2} + \frac{6598691258343}{2} a + 3205391057693 \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 5 a - 4\) , \( 434 a^{3} - 1656 a^{2} + 96 a + 3155\) , \( -12729 a^{3} + 49440 a^{2} - 3800 a - 94931\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(434a^{3}-1656a^{2}+96a+3155\right){x}-12729a^{3}+49440a^{2}-3800a-94931$ |
| 2.1-a3 |
2.1-a |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$12.49752$ |
$(-2a^2+3a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$666.9473147$ |
1.300094701 |
\( \frac{905763}{2} a^{3} - 1441593 a^{2} - \frac{2931531}{2} a + 5361929 \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 6 a + 4\) , \( a + 1\) , \( -5 a^{3} + 5 a^{2} + 30 a\) , \( -5 a^{3} + 9 a^{2} + 27 a - 18\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+6a+4\right){x}^{2}+\left(-5a^{3}+5a^{2}+30a\right){x}-5a^{3}+9a^{2}+27a-18$ |
| 2.1-a4 |
2.1-a |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{4} \) |
$12.49752$ |
$(-2a^2+3a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$333.4736573$ |
1.300094701 |
\( \frac{69987}{2} a^{3} + \frac{121937}{4} a^{2} - 156508 a - \frac{675917}{4} \) |
\( \bigl[1\) , \( a^{3} - 4 a - 3\) , \( a^{3} - a^{2} - 3 a\) , \( 57 a^{3} - 173 a^{2} - 189 a + 645\) , \( -427 a^{3} + 1366 a^{2} + 1377 a - 5075\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(57a^{3}-173a^{2}-189a+645\right){x}-427a^{3}+1366a^{2}+1377a-5075$ |
| 2.2-a1 |
2.2-a |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{2} \) |
$12.49752$ |
$(-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1333.894629$ |
1.300094701 |
\( 229125 a^{3} - \frac{1457903}{2} a^{2} - 740018 a + 2709224 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{2} - 3\) , \( -26 a^{3} - 22 a^{2} + 114 a + 129\) , \( 64 a^{3} + 54 a^{2} - 284 a - 305\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+4\right){x}^{2}+\left(-26a^{3}-22a^{2}+114a+129\right){x}+64a^{3}+54a^{2}-284a-305$ |
| 2.2-a2 |
2.2-a |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2 \) |
$12.49752$ |
$(-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$666.9473147$ |
1.300094701 |
\( \frac{1000078311417}{2} a^{3} - \frac{3184217817083}{2} a^{2} - 1615245279214 a + 5912706089740 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{2} - 3\) , \( -426 a^{3} - 372 a^{2} + 1899 a + 2064\) , \( 10801 a^{3} + 9507 a^{2} - 48234 a - 52519\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+4\right){x}^{2}+\left(-426a^{3}-372a^{2}+1899a+2064\right){x}+10801a^{3}+9507a^{2}-48234a-52519$ |
| 2.2-a3 |
2.2-a |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( -2 \) |
$12.49752$ |
$(-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$666.9473147$ |
1.300094701 |
\( -\frac{905763}{2} a^{3} - \frac{165897}{2} a^{2} + 2990307 a + 2907452 \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + a + 4\) , \( 1\) , \( 2 a^{3} - 13 a - 10\) , \( 5 a^{3} - 34 a - 31\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(2a^{3}-13a-10\right){x}+5a^{3}-34a-31$ |
| 2.2-a4 |
2.2-a |
$4$ |
$4$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{4} \) |
$12.49752$ |
$(-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$333.4736573$ |
1.300094701 |
\( -\frac{69987}{2} a^{3} + \frac{541859}{4} a^{2} - 9441 a - \frac{520019}{2} \) |
\( \bigl[1\) , \( -a^{3} + 4 a + 3\) , \( a^{3} - a^{2} - 3 a\) , \( -54 a^{3} - 7 a^{2} + 359 a + 345\) , \( 402 a^{3} + 70 a^{2} - 2658 a - 2578\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+4a+3\right){x}^{2}+\left(-54a^{3}-7a^{2}+359a+345\right){x}+402a^{3}+70a^{2}-2658a-2578$ |
| 4.2-a1 |
4.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{27} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$122.2454817$ |
4.289323297 |
\( \frac{694282681}{256} a^{3} + \frac{1855061265}{512} a^{2} - \frac{531519125}{64} a - \frac{5327766285}{512} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - a - 3\) , \( 18 a^{3} - 67 a^{2} + 126\) , \( 105 a^{3} - 423 a^{2} + 50 a + 827\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(18a^{3}-67a^{2}+126\right){x}+105a^{3}-423a^{2}+50a+827$ |
| 4.2-a2 |
4.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.509203478$ |
4.289323297 |
\( -16455542779760273679467 a^{3} + \frac{510774891651183682510191}{8} a^{2} - \frac{19363197331776924604393}{4} a - \frac{490175316381217482606011}{4} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -76 a^{3} + 123 a^{2} + 252 a - 490\) , \( -493 a^{3} + 62 a^{2} + 1897 a + 27\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-76a^{3}+123a^{2}+252a-490\right){x}-493a^{3}+62a^{2}+1897a+27$ |
| 4.2-a3 |
4.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{27} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$122.2454817$ |
4.289323297 |
\( -\frac{694282681}{256} a^{3} + \frac{6020757351}{512} a^{2} - \frac{226479101}{32} a - \frac{3168146329}{256} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -26 a^{3} + 83 a^{2} + 82 a - 310\) , \( 187 a^{3} - 606 a^{2} - 599 a + 2255\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-26a^{3}+83a^{2}+82a-310\right){x}+187a^{3}-606a^{2}-599a+2255$ |
| 4.2-a4 |
4.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.509203478$ |
4.289323297 |
\( 16455542779760273679467 a^{3} + \frac{115841864936937114202983}{8} a^{2} - \frac{146972590481141736876097}{2} a - \frac{639946478012887321346353}{8} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 4\) , \( a^{3} - 4 a - 4\) , \( 75 a^{3} - 104 a^{2} - 267 a - 190\) , \( 491 a^{3} - 1414 a^{2} - 538 a + 1490\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(75a^{3}-104a^{2}-267a-190\right){x}+491a^{3}-1414a^{2}-538a+1490$ |
| 4.2-b1 |
4.2-b |
$2$ |
$13$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{26} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/13\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$13$ |
13B.1.1 |
$1$ |
\( 13^{2} \) |
$1$ |
$257.7913978$ |
2.010073198 |
\( \frac{49375}{128} a^{2} - \frac{49375}{128} a - \frac{63875}{64} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a\) , \( a^{3} - 4 a - 4\) , \( 9 a^{3} + 7 a^{2} - 43 a - 45\) , \( -132 a^{3} - 14 a^{2} + 906 a + 873\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-4a-4\right){y}={x}^{3}+a{x}^{2}+\left(9a^{3}+7a^{2}-43a-45\right){x}-132a^{3}-14a^{2}+906a+873$ |
| 4.2-b2 |
4.2-b |
$2$ |
$13$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{2} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$13$ |
13B.1.2 |
$28561$ |
\( 1 \) |
$1$ |
$0.009025993$ |
2.010073198 |
\( -\frac{1015079493993812925625}{2} a^{2} + \frac{1015079493993812925625}{2} a + 1312389394331959267625 \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a\) , \( a^{3} - 4 a - 4\) , \( -5351 a^{3} - 30778 a^{2} - 56018 a - 32105\) , \( -4023405 a^{3} - 9584418 a^{2} - 551003 a + 6105335\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-4a-4\right){y}={x}^{3}+a{x}^{2}+\left(-5351a^{3}-30778a^{2}-56018a-32105\right){x}-4023405a^{3}-9584418a^{2}-551003a+6105335$ |
| 4.2-c1 |
4.2-c |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{19} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1.202728232$ |
$15.87449298$ |
2.679682408 |
\( \frac{102104527429727}{64} a^{3} - \frac{2600784159486829}{512} a^{2} - \frac{659650035947103}{128} a + \frac{4829369743944619}{256} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a^{3} - 4 a - 4\) , \( 0\) , \( -604 a^{3} + 1958 a^{2} + 1940 a - 7285\) , \( -17885 a^{3} + 57010 a^{2} + 57753 a - 211747\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}={x}^{3}+\left(a^{3}-4a-4\right){x}^{2}+\left(-604a^{3}+1958a^{2}+1940a-7285\right){x}-17885a^{3}+57010a^{2}+57753a-211747$ |
| 4.2-c2 |
4.2-c |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.400909410$ |
$1285.833931$ |
2.679682408 |
\( -\frac{25217}{4} a^{3} - \frac{77129}{8} a^{2} + \frac{199157}{4} a + \frac{350093}{4} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a^{3} - 4 a - 4\) , \( 0\) , \( a^{3} + 33 a^{2} - 15 a - 135\) , \( -4 a^{3} + 89 a^{2} - 10 a - 361\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}={x}^{3}+\left(a^{3}-4a-4\right){x}^{2}+\left(a^{3}+33a^{2}-15a-135\right){x}-4a^{3}+89a^{2}-10a-361$ |
| 4.2-c3 |
4.2-c |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.801818821$ |
$642.9169659$ |
2.679682408 |
\( -\frac{51305}{2} a^{3} + \frac{813607}{8} a^{2} - \frac{19441}{2} a - \frac{1573105}{8} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - 4 a^{2} + 2 a + 5\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-a^{3}+2a^{2}+2a-3\right){x}+a^{3}-4a^{2}+2a+5$ |
| 4.2-c4 |
4.2-c |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{11} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.405456464$ |
$7.937246492$ |
2.679682408 |
\( -\frac{102582197674908681}{32} a^{3} + \frac{398014909052294465}{32} a^{2} - \frac{15088527925305755}{16} a - \frac{381962949195933811}{16} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 39 a^{3} - 163 a^{2} + 62 a + 237\) , \( 634 a^{3} - 2497 a^{2} + 382 a + 4467\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(39a^{3}-163a^{2}+62a+237\right){x}+634a^{3}-2497a^{2}+382a+4467$ |
| 4.2-d1 |
4.2-d |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{3} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1097.369024$ |
4.278249938 |
\( \frac{472300529759525}{2} a^{3} + 207802963641450 a^{2} - 1054587380695375 a - \frac{2295936474468319}{2} \) |
\( \bigl[1\) , \( a^{3} - 4 a - 5\) , \( a + 1\) , \( 12 a^{3} - 40 a^{2} - 5 a + 70\) , \( -66 a^{3} + 252 a^{2} - 12 a - 477\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-5\right){x}^{2}+\left(12a^{3}-40a^{2}-5a+70\right){x}-66a^{3}+252a^{2}-12a-477$ |
| 4.2-d2 |
4.2-d |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{3} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1097.369024$ |
4.278249938 |
\( -\frac{472300529759525}{2} a^{3} + \frac{1832507516561475}{2} a^{2} - \frac{138938682453625}{2} a - 1758602389408322 \) |
\( \bigl[1\) , \( -a^{3} + 4 a + 4\) , \( a^{2} - 4\) , \( -10 a^{3} - 7 a^{2} + 45 a + 40\) , \( 79 a^{3} + 69 a^{2} - 353 a - 382\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{3}+4a+4\right){x}^{2}+\left(-10a^{3}-7a^{2}+45a+40\right){x}+79a^{3}+69a^{2}-353a-382$ |
| 4.2-e1 |
4.2-e |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{9} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.400909410$ |
$1285.833931$ |
2.679682408 |
\( \frac{25217}{4} a^{3} - \frac{228431}{8} a^{2} - \frac{46377}{4} a + \frac{970937}{8} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 5 a + 4\) , \( a + 1\) , \( -4 a^{3} + 4 a^{2} + 17 a + 8\) , \( -5 a^{3} + 16 a^{2} + 4 a - 26\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+5a+4\right){x}^{2}+\left(-4a^{3}+4a^{2}+17a+8\right){x}-5a^{3}+16a^{2}+4a-26$ |
| 4.2-e2 |
4.2-e |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{19} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1.202728232$ |
$15.87449298$ |
2.679682408 |
\( -\frac{102104527429727}{64} a^{3} - \frac{150275501173381}{512} a^{2} + \frac{2694829902224311}{256} a + \frac{5236191404051813}{512} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 5 a + 4\) , \( a + 1\) , \( 21 a^{3} - 46 a^{2} - 73 a + 13\) , \( 234 a^{3} - 487 a^{2} - 734 a + 202\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+5a+4\right){x}^{2}+\left(21a^{3}-46a^{2}-73a+13\right){x}+234a^{3}-487a^{2}-734a+202$ |
| 4.2-e3 |
4.2-e |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.801818821$ |
$642.9169659$ |
2.679682408 |
\( \frac{51305}{2} a^{3} + \frac{197947}{8} a^{2} - \frac{466895}{4} a - \frac{521241}{4} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 4\) , \( -a^{3} + 4 a + 5\) , \( -a^{3} - a^{2} + 3 a + 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-a^{3}+4a+5\right){x}-a^{3}-a^{2}+3a+3$ |
| 4.2-e4 |
4.2-e |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{11} \) |
$13.62864$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.405456464$ |
$7.937246492$ |
2.679682408 |
\( \frac{102582197674908681}{32} a^{3} + \frac{45134158013784211}{16} a^{2} - \frac{458106169229251377}{32} a - \frac{124667560716273337}{8} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 4\) , \( -41 a^{3} - 45 a^{2} + 154 a + 180\) , \( -594 a^{3} - 550 a^{2} + 2560 a + 2810\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-41a^{3}-45a^{2}+154a+180\right){x}-594a^{3}-550a^{2}+2560a+2810$ |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 11 \) |
$1$ |
$103.5416837$ |
2.220196267 |
\( \frac{355340625}{64} a^{3} - \frac{1159260467}{64} a^{2} - \frac{554519513}{32} a + \frac{2186610393}{32} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{3} - a^{2} - 3 a\) , \( -5 a^{3} - 27 a^{2} - 31 a - 6\) , \( -378 a^{3} - 453 a^{2} + 1327 a + 1579\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+4\right){x}^{2}+\left(-5a^{3}-27a^{2}-31a-6\right){x}-378a^{3}-453a^{2}+1327a+1579$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{30} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 11 \) |
$1$ |
$51.77084188$ |
2.220196267 |
\( -\frac{843443}{1024} a^{3} + \frac{5973299}{2048} a^{2} + \frac{455801}{256} a - \frac{10234669}{1024} \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( 0\) , \( -24 a^{3} + 77 a^{2} + 96 a - 324\) , \( -218 a^{3} + 703 a^{2} + 678 a - 2562\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-24a^{3}+77a^{2}+96a-324\right){x}-218a^{3}+703a^{2}+678a-2562$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{5} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1459.291686$ |
2.844628574 |
\( \frac{4957121}{2} a^{3} - \frac{15774715}{2} a^{2} - 8007161 a + 29290945 \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{3} - 4 a - 4\) , \( -5 a^{3} - 4 a^{2} + 21 a + 25\) , \( a^{3} + 2 a^{2} - 10 a - 14\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-4a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-5a^{3}-4a^{2}+21a+25\right){x}+a^{3}+2a^{2}-10a-14$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$729.6458431$ |
2.844628574 |
\( -9963 a^{3} + \frac{75443}{2} a^{2} - 312 a - 73937 \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a\) , \( 3 a^{2} + 4 a + 1\) , \( 45 a^{3} + 36 a^{2} - 207 a - 221\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(3a^{2}+4a+1\right){x}+45a^{3}+36a^{2}-207a-221$ |
| 8.2-a1 |
8.2-a |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{15} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 11 \) |
$1$ |
$103.5416837$ |
2.220196267 |
\( -\frac{355340625}{64} a^{3} - 1456853 a^{2} + \frac{2361538085}{64} a + \frac{1230130959}{32} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 19 a^{3} - 58 a^{2} + 65 a - 63\) , \( 226 a^{3} - 904 a^{2} + 612 a + 621\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(19a^{3}-58a^{2}+65a-63\right){x}+226a^{3}-904a^{2}+612a+621$ |
| 8.2-a2 |
8.2-a |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{30} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 11 \) |
$1$ |
$51.77084188$ |
2.220196267 |
\( \frac{843443}{1024} a^{3} + \frac{912641}{2048} a^{2} - \frac{2633087}{512} a - \frac{12536517}{2048} \) |
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a^{2} - 3\) , \( 26 a^{3} - 181 a - 167\) , \( 245 a^{3} + 44 a^{2} - 1623 a - 1579\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(26a^{3}-181a-167\right){x}+245a^{3}+44a^{2}-1623a-1579$ |
| 8.2-b1 |
8.2-b |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$729.6458431$ |
2.844628574 |
\( 9963 a^{3} + \frac{15665}{2} a^{2} - 45242 a - \frac{92981}{2} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 6 a - 4\) , \( a^{3} - 5 a - 4\) , \( -81 a^{3} + 372 a^{2} - 79 a - 748\) , \( -7522 a^{3} + 29382 a^{2} - 2414 a - 56530\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{3}-6a-4\right){x}^{2}+\left(-81a^{3}+372a^{2}-79a-748\right){x}-7522a^{3}+29382a^{2}-2414a-56530$ |
| 8.2-b2 |
8.2-b |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{5} \) |
$14.86214$ |
$(-2a^2+3a+8), (-2a^3-2a^2+9a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1459.291686$ |
2.844628574 |
\( -\frac{4957121}{2} a^{3} - 451676 a^{2} + \frac{32692389}{2} a + 15874987 \) |
\( \bigl[a^{3} - 4 a - 3\) , \( -a^{3} + 4 a + 5\) , \( a^{3} - 4 a - 3\) , \( 6 a^{3} - 16 a^{2} - 2 a + 22\) , \( -3 a^{3} + 43 a^{2} - 29 a - 109\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+4a+5\right){x}^{2}+\left(6a^{3}-16a^{2}-2a+22\right){x}-3a^{3}+43a^{2}-29a-109$ |
| 14.1-a1 |
14.1-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{8} \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$107.0965491$ |
0.835062398 |
\( \frac{14458703259130405}{11529602} a^{3} - \frac{46731870616554379}{11529602} a^{2} - \frac{6572760949165545}{1647086} a + \frac{174733844109527187}{11529602} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - a - 4\) , \( 4 a^{3} - 7 a^{2} - 13 a + 2\) , \( 8 a^{3} - 51 a^{2} + 36 a + 126\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(4a^{3}-7a^{2}-13a+2\right){x}+8a^{3}-51a^{2}+36a+126$ |
| 14.1-a2 |
14.1-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$428.3861965$ |
0.835062398 |
\( -\frac{31270700}{2401} a^{3} + \frac{548687607}{9604} a^{2} - \frac{26911991}{686} a - \frac{358506179}{9604} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - a - 4\) , \( 4 a^{3} - 12 a^{2} - 3 a + 22\) , \( 7 a^{3} - 27 a^{2} + 2 a + 52\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(4a^{3}-12a^{2}-3a+22\right){x}+7a^{3}-27a^{2}+2a+52$ |
| 14.1-a3 |
14.1-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{16} \cdot 7 \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$214.1930982$ |
0.835062398 |
\( -\frac{17579977}{896} a^{3} + \frac{129307207}{1792} a^{2} - \frac{67981}{32} a - \frac{241298523}{1792} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 5 a - 4\) , \( 10 a^{3} - 32 a^{2} - 6 a + 60\) , \( -38 a^{3} + 159 a^{2} - 26 a - 312\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(10a^{3}-32a^{2}-6a+60\right){x}-38a^{3}+159a^{2}-26a-312$ |
| 14.1-a4 |
14.1-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{4} \cdot 7 \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$53.54827456$ |
0.835062398 |
\( \frac{9678122621468708}{7} a^{3} + \frac{34065475366550991}{28} a^{2} - \frac{12348585612935167}{2} a - \frac{188188276875044715}{28} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 3 a - 1\) , \( a\) , \( -73 a^{3} + 194 a^{2} + 246 a - 700\) , \( 457 a^{3} - 1904 a^{2} - 1338 a + 7242\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-3a-1\right){x}^{2}+\left(-73a^{3}+194a^{2}+246a-700\right){x}+457a^{3}-1904a^{2}-1338a+7242$ |
| 14.1-a5 |
14.1-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$428.3861965$ |
0.835062398 |
\( \frac{3972311827}{392} a^{3} + \frac{6991088289}{784} a^{2} - \frac{1267075049}{28} a - \frac{38618238293}{784} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 3 a - 1\) , \( a\) , \( -3 a^{3} + 19 a^{2} + 6 a - 70\) , \( 3 a^{3} - 6 a^{2} - 10 a + 18\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-3a-1\right){x}^{2}+\left(-3a^{3}+19a^{2}+6a-70\right){x}+3a^{3}-6a^{2}-10a+18$ |
| 14.1-a6 |
14.1-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{2} \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$107.0965491$ |
0.835062398 |
\( -\frac{764745453397}{98} a^{3} + \frac{2967182405835}{98} a^{2} - \frac{32138361191}{14} a - \frac{5695031599203}{98} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{3} - 4 a - 4\) , \( 2\) , \( -3 a^{3} + 4 a^{2} + 12 a - 14\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+2{x}-3a^{3}+4a^{2}+12a-14$ |
| 14.1-b1 |
14.1-b |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{2} \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$603.8161404$ |
2.354063499 |
\( -\frac{1487}{98} a^{3} + \frac{81574}{49} a^{2} - \frac{26343}{14} a - \frac{180780}{49} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( 1\) , \( 3 a^{2} - 2\) , \( a^{3} + 3 a^{2} - 5 a - 9\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(3a^{2}-2\right){x}+a^{3}+3a^{2}-5a-9$ |
| 14.1-b2 |
14.1-b |
$2$ |
$2$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$15.93900$ |
$(-2a^2+3a+8), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$603.8161404$ |
2.354063499 |
\( -\frac{97157}{7} a^{3} - \frac{49215}{14} a^{2} + 92585 a + \frac{1325099}{14} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{2} - 3\) , \( -10 a^{3} + 39 a^{2} + 30 a - 147\) , \( 28 a^{3} - 81 a^{2} - 93 a + 297\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-10a^{3}+39a^{2}+30a-147\right){x}+28a^{3}-81a^{2}-93a+297$ |
| 14.2-a1 |
14.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{3} \) |
$15.93900$ |
$(-2a^2+3a+8), (a^3+a^2-4a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$666.4769028$ |
2.598355434 |
\( -\frac{27204101}{1372} a^{3} - \frac{12538321}{2744} a^{2} + \frac{44619962}{343} a + \frac{50554123}{392} \) |
\( \bigl[a^{3} - 4 a - 3\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 14 a^{3} + 11 a^{2} - 64 a - 68\) , \( 30 a^{3} + 73 a^{2} - 183 a - 271\bigr] \) |
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(14a^{3}+11a^{2}-64a-68\right){x}+30a^{3}+73a^{2}-183a-271$ |
| 14.2-a2 |
14.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7^{6} \) |
$15.93900$ |
$(-2a^2+3a+8), (a^3+a^2-4a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$666.4769028$ |
2.598355434 |
\( \frac{2606982251193}{470596} a^{3} + \frac{576628151593}{117649} a^{2} - \frac{11654886408037}{470596} a - \frac{907473417471}{33614} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 51 a^{3} - 198 a^{2} + 20 a + 372\) , \( -508 a^{3} + 1972 a^{2} - 151 a - 3783\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(51a^{3}-198a^{2}+20a+372\right){x}-508a^{3}+1972a^{2}-151a-3783$ |
| 14.2-a3 |
14.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{18} \) |
$15.93900$ |
$(-2a^2+3a+8), (a^3+a^2-4a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$8.228109911$ |
2.598355434 |
\( \frac{34286071190041343029089}{3256827195820898} a^{3} - \frac{9145034796565542227590}{1628413597910449} a^{2} - \frac{201653019260377581104269}{3256827195820898} a - \frac{6180592031830217024959}{232630513987207} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 351 a^{3} - 1403 a^{2} + 325 a + 2322\) , \( 11178 a^{3} - 43805 a^{2} + 5513 a + 80445\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(351a^{3}-1403a^{2}+325a+2322\right){x}+11178a^{3}-43805a^{2}+5513a+80445$ |
| 14.2-a4 |
14.2-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{9} \) |
$15.93900$ |
$(-2a^2+3a+8), (a^3+a^2-4a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$8.228109911$ |
2.598355434 |
\( -\frac{26381558016500003829093}{40353607} a^{3} - \frac{9707323578554132916593}{80707214} a^{2} + \frac{174070609015258362810152}{40353607} a + \frac{48318328770334256002667}{11529602} \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{2} - a - 3\) , \( -52 a^{3} + 242 a^{2} + 144 a - 926\) , \( -928 a^{3} + 2949 a^{2} + 3000 a - 10951\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(-52a^{3}+242a^{2}+144a-926\right){x}-928a^{3}+2949a^{2}+3000a-10951$ |
| 14.3-a1 |
14.3-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{9} \) |
$15.93900$ |
$(-2a^3-2a^2+9a+11), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$8.228109911$ |
2.598355434 |
\( \frac{26381558016500003829093}{40353607} a^{3} - \frac{167996671677554155891151}{80707214} a^{2} - \frac{12174087341029174058040}{5764801} a + \frac{311949539905651188532097}{40353607} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{2} - 2 a - 4\) , \( a^{2} - a - 3\) , \( -645 a^{3} + 2520 a^{2} - 212 a - 4854\) , \( 1639 a^{3} - 6337 a^{2} + 454 a + 12141\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-645a^{3}+2520a^{2}-212a-4854\right){x}+1639a^{3}-6337a^{2}+454a+12141$ |
| 14.3-a2 |
14.3-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{3} \) |
$15.93900$ |
$(-2a^3-2a^2+9a+11), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$666.4769028$ |
2.598355434 |
\( \frac{27204101}{1372} a^{3} - \frac{175762927}{2744} a^{2} - \frac{3011758}{49} a + \frac{321946017}{1372} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -30 a^{3} + 92 a^{2} + 98 a - 336\) , \( -185 a^{3} + 588 a^{2} + 597 a - 2183\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-30a^{3}+92a^{2}+98a-336\right){x}-185a^{3}+588a^{2}+597a-2183$ |
| 14.3-a3 |
14.3-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7^{6} \) |
$15.93900$ |
$(-2a^3-2a^2+9a+11), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$666.4769028$ |
2.598355434 |
\( -\frac{2606982251193}{470596} a^{3} + \frac{10127459359951}{470596} a^{2} - \frac{55648968449}{33614} a - \frac{9723009697533}{235298} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -51 a^{3} - 46 a^{2} + 224 a + 245\) , \( 559 a^{3} + 493 a^{2} - 2493 a - 2715\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-51a^{3}-46a^{2}+224a+245\right){x}+559a^{3}+493a^{2}-2493a-2715$ |
| 14.3-a4 |
14.3-a |
$4$ |
$6$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( - 2 \cdot 7^{18} \) |
$15.93900$ |
$(-2a^3-2a^2+9a+11), (-a^3+3a^2+2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$8.228109911$ |
2.598355434 |
\( -\frac{34286071190041343029089}{3256827195820898} a^{3} + \frac{84568143976992944632087}{3256827195820898} a^{2} + \frac{9669638919751122923383}{232630513987207} a - \frac{136092653054545180439893}{1628413597910449} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -351 a^{3} - 351 a^{2} + 1429 a + 1595\) , \( -10827 a^{3} - 9921 a^{2} + 47134 a + 51736\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-351a^{3}-351a^{2}+1429a+1595\right){x}-10827a^{3}-9921a^{2}+47134a+51736$ |
| 14.4-a1 |
14.4-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( - 2^{16} \cdot 7 \) |
$15.93900$ |
$(-2a^3-2a^2+9a+11), (a^3+a^2-4a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$214.1930982$ |
0.835062398 |
\( \frac{17579977}{896} a^{3} + \frac{23827345}{1792} a^{2} - \frac{583311}{7} a - \frac{10782729}{128} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a^{3} - 4 a - 5\) , \( a\) , \( -2 a^{3} + 9 a + 9\) , \( -a^{2} + a + 2\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a-5\right){x}^{2}+\left(-2a^{3}+9a+9\right){x}-a^{2}+a+2$ |
| 14.4-a2 |
14.4-a |
$6$ |
$8$ |
4.4.16448.2 |
$4$ |
$[4, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( - 2^{4} \cdot 7 \) |
$15.93900$ |
$(-2a^3-2a^2+9a+11), (a^3+a^2-4a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$53.54827456$ |
0.835062398 |
\( -\frac{9678122621468708}{7} a^{3} + \frac{150202946824175487}{28} a^{2} - \frac{2847055902408535}{7} a - \frac{20592179257407945}{2} \) |
\( \bigl[a^{3} - 5 a - 3\) , \( a^{3} - 5 a - 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 81 a^{3} - 32 a^{2} - 437 a - 340\) , \( -554 a^{3} - 330 a^{2} + 4081 a + 4373\bigr] \) |
${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-5a-4\right){x}^{2}+\left(81a^{3}-32a^{2}-437a-340\right){x}-554a^{3}-330a^{2}+4081a+4373$ |
*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.
