| 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 |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{31} \) |
$12.49752$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$176.7368730$ |
1.378067905 |
\( -\frac{841987}{256} a^{3} + \frac{1200957}{256} a^{2} + \frac{5749579}{256} a + \frac{801315}{64} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 1\) , \( -a^{3} + 3 a^{2} + 3 a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 132 a^{3} - 190 a^{2} - 903 a - 493\) , \( 1789 a^{3} - 2606 a^{2} - 12153 a - 6593\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+1\right){x}{y}+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-3\right){x}^{2}+\left(132a^{3}-190a^{2}-903a-493\right){x}+1789a^{3}-2606a^{2}-12153a-6593$ |
| 2.1-b1 |
2.1-b |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{31} \) |
$12.49752$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 31 \) |
$0.014287432$ |
$203.1116684$ |
2.805783741 |
\( -\frac{841987}{256} a^{3} + \frac{1200957}{256} a^{2} + \frac{5749579}{256} a + \frac{801315}{64} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 7 a + 1\) , \( 1\) , \( a + 1\) , \( 6 a^{2} - 17 a - 12\) , \( 16 a^{3} - 59 a^{2} - 3 a + 33\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(6a^{2}-17a-12\right){x}+16a^{3}-59a^{2}-3a+33$ |
| 4.1-a1 |
4.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.914495295$ |
$115.8631482$ |
2.478514741 |
\( -16800495556 a^{3} + 24508705228 a^{2} + 114016509456 a + 61852179108 \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( 2 a^{3} - 5 a^{2} - 8 a + 1\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( 31 a^{3} - 45 a^{2} - 211 a - 115\) , \( 166 a^{3} - 243 a^{2} - 1124 a - 610\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}+\left(a^{3}-3a^{2}-2a+2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-8a+1\right){x}^{2}+\left(31a^{3}-45a^{2}-211a-115\right){x}+166a^{3}-243a^{2}-1124a-610$ |
| 4.1-a2 |
4.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.228623823$ |
$1853.810371$ |
2.478514741 |
\( 12288 a^{2} + 8192 a - 8192 \) |
\( \bigl[0\) , \( -a^{2} + a + 3\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 4 a^{3} - 14 a^{2} + 7\) , \( -10 a^{3} + 33 a^{2} + 11 a - 15\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(4a^{3}-14a^{2}+7\right){x}-10a^{3}+33a^{2}+11a-15$ |
| 4.1-a3 |
4.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 3 \) |
$0.457247647$ |
$926.9051856$ |
2.478514741 |
\( 18251776 a^{3} - 49274848 a^{2} - 75104256 a + 52712176 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -a^{3} + 3 a^{2} + 4 a - 2\) , \( 0\) , \( -a^{3} + 3 a^{2} + 4 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+2\right){x}{y}={x}^{3}+\left(-a^{3}+3a^{2}+4a-2\right){x}^{2}+\left(-a^{3}+3a^{2}+4a+1\right){x}$ |
| 4.1-a4 |
4.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.228623823$ |
$463.4525928$ |
2.478514741 |
\( 1371554665152452 a^{3} - 3698538392272844 a^{2} - 5652915138723344 a + 3937837510673452 \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 2\) , \( -a^{3} + 3 a^{2} + 2 a - 3\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( 14 a^{3} - 15 a^{2} - 100 a - 63\) , \( -4 a^{3} + 6 a^{2} + 14 a + 1\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-3\right){x}^{2}+\left(14a^{3}-15a^{2}-100a-63\right){x}-4a^{3}+6a^{2}+14a+1$ |
| 4.1-b1 |
4.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.816035709$ |
$1307.486747$ |
2.079839964 |
\( 12288 a^{2} + 8192 a - 8192 \) |
\( \bigl[0\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -6 a^{3} + 17 a^{2} + 22 a - 16\) , \( -13 a^{3} + 35 a^{2} + 54 a - 40\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+2\right){x}^{2}+\left(-6a^{3}+17a^{2}+22a-16\right){x}-13a^{3}+35a^{2}+54a-40$ |
| 4.1-b2 |
4.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$3.264142836$ |
$81.71792169$ |
2.079839964 |
\( 1371554665152452 a^{3} - 3698538392272844 a^{2} - 5652915138723344 a + 3937837510673452 \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 3 a^{2} - 1\) , \( 2 a^{3} - 9 a^{2} - 5 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(3a^{2}-1\right){x}+2a^{3}-9a^{2}-5a+1$ |
| 4.1-b3 |
4.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.816035709$ |
$326.8716867$ |
2.079839964 |
\( -16800495556 a^{3} + 24508705228 a^{2} + 114016509456 a + 61852179108 \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a + 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 164 a^{3} - 567 a^{2} - 152 a + 220\) , \( 2549 a^{3} - 8828 a^{2} - 2381 a + 3483\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){x}{y}+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a+1\right){x}^{2}+\left(164a^{3}-567a^{2}-152a+220\right){x}+2549a^{3}-8828a^{2}-2381a+3483$ |
| 4.1-b4 |
4.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$13.62864$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1.632071418$ |
$653.7433735$ |
2.079839964 |
\( 18251776 a^{3} - 49274848 a^{2} - 75104256 a + 52712176 \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 2\) , \( 2 a^{3} - 5 a^{2} - 8 a\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( 3 a^{3} - 4 a^{2} - 20 a - 22\) , \( -31 a^{3} + 53 a^{2} + 194 a + 68\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+2\right){x}{y}+\left(a^{3}-3a^{2}-2a+2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-8a\right){x}^{2}+\left(3a^{3}-4a^{2}-20a-22\right){x}-31a^{3}+53a^{2}+194a+68$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$14.86214$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$289.8365604$ |
2.259938487 |
\( -3347 a^{3} + 6717 a^{2} + 17259 a + 380 \) |
\( \bigl[a\) , \( -a^{3} + 3 a^{2} + 3 a - 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( -a + 1\) , \( -a^{3} + 3 a^{2} + 2 a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-1\right){x}^{2}+\left(-a+1\right){x}-a^{3}+3a^{2}+2a-4$ |
| 8.1-b1 |
8.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$14.86214$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$98.59944108$ |
1.537616037 |
\( -19732064944188 a^{3} + 28755721617264 a^{2} + 133997853671424 a + 72719387509556 \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( -a^{3} + 3 a^{2} + 3 a - 1\) , \( a^{3} - 2 a^{2} - 5 a\) , \( 180 a^{3} - 260 a^{2} - 1229 a - 672\) , \( 2832 a^{3} - 4126 a^{2} - 19235 a - 10441\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-1\right){x}^{2}+\left(180a^{3}-260a^{2}-1229a-672\right){x}+2832a^{3}-4126a^{2}-19235a-10441$ |
| 8.1-b2 |
8.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$14.86214$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$394.3977643$ |
1.537616037 |
\( -174080 a^{3} + 604160 a^{2} + 159744 a - 239616 \) |
\( \bigl[0\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 4 a^{3} - 14 a^{2} - 6 a + 7\) , \( 6 a^{3} - 18 a^{2} - 5 a + 7\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+2\right){x}^{2}+\left(4a^{3}-14a^{2}-6a+7\right){x}+6a^{3}-18a^{2}-5a+7$ |
| 8.1-b3 |
8.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$14.86214$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1577.591057$ |
1.537616037 |
\( 6918173802044 a^{3} + 11184587375248 a^{2} - 1057784853504 a - 3825686656612 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 0\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( -4 a^{3} + 14 a^{2} + 17 a - 28\) , \( 12 a^{3} - 26 a^{2} - 58 a + 6\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){x}{y}+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(-4a^{3}+14a^{2}+17a-28\right){x}+12a^{3}-26a^{2}-58a+6$ |
| 8.1-b4 |
8.1-b |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$14.86214$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$788.7955286$ |
1.537616037 |
\( -1286304 a^{3} + 2859552 a^{2} + 10862784 a + 5747216 \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 2\) , \( -2 a^{3} + 5 a^{2} + 9 a - 1\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -2 a^{3} + 5 a^{2} + 6 a + 3\) , \( -a^{2} + a\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+2\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+9a-1\right){x}^{2}+\left(-2a^{3}+5a^{2}+6a+3\right){x}-a^{2}+a$ |
| 8.1-c1 |
8.1-c |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$14.86214$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.162934716$ |
$562.8517423$ |
2.860296709 |
\( -3347 a^{3} + 6717 a^{2} + 17259 a + 380 \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 2\) , \( -a^{3} + 2 a^{2} + 5 a + 1\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 3 a^{3} - 3 a^{2} - 23 a - 16\) , \( 15 a^{3} - 22 a^{2} - 104 a - 57\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a+1\right){x}^{2}+\left(3a^{3}-3a^{2}-23a-16\right){x}+15a^{3}-22a^{2}-104a-57$ |
| 8.1-d1 |
8.1-d |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$14.86214$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.111590319$ |
$1215.568796$ |
2.115336742 |
\( 6918173802044 a^{3} + 11184587375248 a^{2} - 1057784853504 a - 3825686656612 \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( 0\) , \( 398 a^{3} - 1378 a^{2} - 370 a + 547\) , \( -8934 a^{3} + 30936 a^{2} + 8355 a - 12216\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}={x}^{3}+\left(a^{3}-3a^{2}-2a+3\right){x}^{2}+\left(398a^{3}-1378a^{2}-370a+547\right){x}-8934a^{3}+30936a^{2}+8355a-12216$ |
| 8.1-d2 |
8.1-d |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$14.86214$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.111590319$ |
$1215.568796$ |
2.115336742 |
\( -174080 a^{3} + 604160 a^{2} + 159744 a - 239616 \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a\) , \( -a^{2} + 2 a + 5\) , \( -a - 2\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}+2a+5\right){x}-a-2$ |
| 8.1-d3 |
8.1-d |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$14.86214$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.223180639$ |
$2431.137593$ |
2.115336742 |
\( -1286304 a^{3} + 2859552 a^{2} + 10862784 a + 5747216 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( a^{2} - 2 a - 2\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( 3 a^{3} + a^{2} - 32 a - 34\) , \( -17 a^{3} + 29 a^{2} + 106 a + 44\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+2\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(3a^{3}+a^{2}-32a-34\right){x}-17a^{3}+29a^{2}+106a+44$ |
| 8.1-d4 |
8.1-d |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$14.86214$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.446361279$ |
$1215.568796$ |
2.115336742 |
\( -19732064944188 a^{3} + 28755721617264 a^{2} + 133997853671424 a + 72719387509556 \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( -2 a^{3} + 18 a^{2} - 27 a - 30\) , \( -9 a^{3} - 5 a^{2} + 114 a + 76\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){x}{y}+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a\right){x}^{2}+\left(-2a^{3}+18a^{2}-27a-30\right){x}-9a^{3}-5a^{2}+114a+76$ |
| 10.1-a1 |
10.1-a |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{4} \) |
$15.28252$ |
$(a), (-2a^3+5a^2+9a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.005502615$ |
$2194.334899$ |
3.765958694 |
\( \frac{100210679}{2500} a^{3} - \frac{90943874}{625} a^{2} - \frac{18207153}{625} a + \frac{79650407}{1250} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 3\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 66 a^{3} - 99 a^{2} - 441 a - 230\) , \( -516 a^{3} + 750 a^{2} + 3510 a + 1912\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+3\right){x}{y}+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+2\right){x}^{2}+\left(66a^{3}-99a^{2}-441a-230\right){x}-516a^{3}+750a^{2}+3510a+1912$ |
| 10.1-b1 |
10.1-b |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{4} \) |
$15.28252$ |
$(a), (-2a^3+5a^2+9a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.021941483$ |
$724.7407107$ |
1.983864792 |
\( \frac{100210679}{2500} a^{3} - \frac{90943874}{625} a^{2} - \frac{18207153}{625} a + \frac{79650407}{1250} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a - 1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -a^{3} + 4 a^{2} - 3 a - 3\) , \( 3 a^{3} - 32 a - 27\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a-1\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-1\right){x}^{2}+\left(-a^{3}+4a^{2}-3a-3\right){x}+3a^{3}-32a-27$ |
| 16.1-a1 |
16.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$704.2521975$ |
1.372813909 |
\( 1371554665152452 a^{3} - 3698538392272844 a^{2} - 5652915138723344 a + 3937837510673452 \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a^{2} - 3 a - 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 4 a^{2} - 2 a - 5\) , \( -2 a^{3} + 8 a^{2} + 3 a - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(4a^{2}-2a-5\right){x}-2a^{3}+8a^{2}+3a-3$ |
| 16.1-a2 |
16.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$704.2521975$ |
1.372813909 |
\( 12288 a^{2} + 8192 a - 8192 \) |
\( \bigl[0\) , \( -a^{3} + 3 a^{2} + 2 a - 2\) , \( a\) , \( -6 a^{3} + 17 a^{2} + 22 a - 16\) , \( 13 a^{3} - 35 a^{2} - 55 a + 38\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-2\right){x}^{2}+\left(-6a^{3}+17a^{2}+22a-16\right){x}+13a^{3}-35a^{2}-55a+38$ |
| 16.1-a3 |
16.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$704.2521975$ |
1.372813909 |
\( -16800495556 a^{3} + 24508705228 a^{2} + 114016509456 a + 61852179108 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 7 a + 2\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 168 a^{3} - 576 a^{2} - 164 a + 226\) , \( -2217 a^{3} + 7685 a^{2} + 2061 a - 3040\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){x}{y}+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+2\right){x}^{2}+\left(168a^{3}-576a^{2}-164a+226\right){x}-2217a^{3}+7685a^{2}+2061a-3040$ |
| 16.1-a4 |
16.1-a |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1408.504395$ |
1.372813909 |
\( 18251776 a^{3} - 49274848 a^{2} - 75104256 a + 52712176 \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 2\) , \( 2 a^{3} - 5 a^{2} - 7 a + 1\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( 3 a^{3} - 2 a^{2} - 22 a - 26\) , \( 8 a^{3} - 12 a^{2} - 52 a - 28\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+2\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-7a+1\right){x}^{2}+\left(3a^{3}-2a^{2}-22a-26\right){x}+8a^{3}-12a^{2}-52a-28$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{43} \) |
$16.20728$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$79.88279633$ |
2.491475964 |
\( -\frac{841987}{256} a^{3} + \frac{1200957}{256} a^{2} + \frac{5749579}{256} a + \frac{801315}{64} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 6 a + 2\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( 11 a^{3} - 17 a^{2} - 71 a - 36\) , \( -19 a^{3} + 27 a^{2} + 132 a + 71\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-3a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+6a+2\right){x}^{2}+\left(11a^{3}-17a^{2}-71a-36\right){x}-19a^{3}+27a^{2}+132a+71$ |
| 16.1-c1 |
16.1-c |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.910967572$ |
$2033.531646$ |
3.611081691 |
\( -174080 a^{3} + 604160 a^{2} + 159744 a - 239616 \) |
\( \bigl[0\) , \( -a^{3} + 3 a^{2} + 4 a - 2\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 4 a^{3} - 14 a^{2} - 6 a + 7\) , \( -6 a^{3} + 17 a^{2} + 7 a - 10\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+4a-2\right){x}^{2}+\left(4a^{3}-14a^{2}-6a+7\right){x}-6a^{3}+17a^{2}+7a-10$ |
| 16.1-c2 |
16.1-c |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.910967572$ |
$508.3829116$ |
3.611081691 |
\( -19732064944188 a^{3} + 28755721617264 a^{2} + 133997853671424 a + 72719387509556 \) |
\( \bigl[a\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( 0\) , \( 182 a^{3} - 266 a^{2} - 1235 a - 667\) , \( -2651 a^{3} + 3863 a^{2} + 18003 a + 9771\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{3}-3a^{2}-4a+2\right){x}^{2}+\left(182a^{3}-266a^{2}-1235a-667\right){x}-2651a^{3}+3863a^{2}+18003a+9771$ |
| 16.1-c3 |
16.1-c |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$3.643870291$ |
$127.0957279$ |
3.611081691 |
\( 6918173802044 a^{3} + 11184587375248 a^{2} - 1057784853504 a - 3825686656612 \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 2\) , \( -a^{2} + 2 a + 3\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( -4 a^{3} + 11 a^{2} + 21 a - 26\) , \( -20 a^{3} + 51 a^{2} + 92 a - 63\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){x}{y}+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-4a^{3}+11a^{2}+21a-26\right){x}-20a^{3}+51a^{2}+92a-63$ |
| 16.1-c4 |
16.1-c |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1.821935145$ |
$1016.765823$ |
3.611081691 |
\( -1286304 a^{3} + 2859552 a^{2} + 10862784 a + 5747216 \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 2\) , \( -1\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 4 a^{2}\) , \( a^{3} - 4 a^{2} + 2\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+2\right){x}{y}+\left(a^{3}-3a^{2}-2a+2\right){y}={x}^{3}-{x}^{2}+\left(a^{3}-4a^{2}\right){x}+a^{3}-4a^{2}+2$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{11} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.062725770$ |
$442.5845583$ |
3.463424259 |
\( -3347 a^{3} + 6717 a^{2} + 17259 a + 380 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 7 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 7 a^{3} - 13 a^{2} - 41 a - 12\) , \( -5 a^{3} + 6 a^{2} + 38 a + 27\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+2\right){x}^{2}+\left(7a^{3}-13a^{2}-41a-12\right){x}-5a^{3}+6a^{2}+38a+27$ |
| 16.1-e1 |
16.1-e |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{11} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.074668382$ |
$859.4826320$ |
4.003199968 |
\( -3347 a^{3} + 6717 a^{2} + 17259 a + 380 \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( a^{3} - 2 a^{2} - 6 a - 2\) , \( a^{3} - 3 a^{2} - 2 a - 2\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+2\right){x}^{2}+\left(a^{3}-2a^{2}-6a-2\right){x}+a^{3}-3a^{2}-2a-2$ |
| 16.1-f1 |
16.1-f |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.832703119$ |
$659.7901633$ |
2.357118495 |
\( -174080 a^{3} + 604160 a^{2} + 159744 a - 239616 \) |
\( \bigl[0\) , \( -a^{2} + a + 4\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -a^{2} + 2 a + 5\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{2}+2a+5\right){x}$ |
| 16.1-f2 |
16.1-f |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.832703119$ |
$164.9475408$ |
2.357118495 |
\( 6918173802044 a^{3} + 11184587375248 a^{2} - 1057784853504 a - 3825686656612 \) |
\( \bigl[a\) , \( -a^{3} + 3 a^{2} + 4 a - 2\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 399 a^{3} - 1381 a^{2} - 373 a + 546\) , \( 8750 a^{3} - 30298 a^{2} - 8181 a + 11962\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+4a-2\right){x}^{2}+\left(399a^{3}-1381a^{2}-373a+546\right){x}+8750a^{3}-30298a^{2}-8181a+11962$ |
| 16.1-f3 |
16.1-f |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$3.665406239$ |
$329.8950816$ |
2.357118495 |
\( -1286304 a^{3} + 2859552 a^{2} + 10862784 a + 5747216 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -a^{3} + 2 a^{2} + 6 a + 2\) , \( 0\) , \( a^{3} + a^{2} - 12 a - 13\) , \( 24 a^{3} - 29 a^{2} - 176 a - 119\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+2\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+6a+2\right){x}^{2}+\left(a^{3}+a^{2}-12a-13\right){x}+24a^{3}-29a^{2}-176a-119$ |
| 16.1-f4 |
16.1-f |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$7.330812479$ |
$41.23688520$ |
2.357118495 |
\( -19732064944188 a^{3} + 28755721617264 a^{2} + 133997853671424 a + 72719387509556 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 2 a^{3} - 5 a^{2} - 9 a\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( 12 a^{2} - 37 a - 25\) , \( -7 a^{3} + 39 a^{2} - 40 a - 43\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-9a\right){x}^{2}+\left(12a^{2}-37a-25\right){x}-7a^{3}+39a^{2}-40a-43$ |
| 16.1-g1 |
16.1-g |
$1$ |
$1$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{43} \) |
$16.20728$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$69.50972214$ |
1.083974334 |
\( -\frac{841987}{256} a^{3} + \frac{1200957}{256} a^{2} + \frac{5749579}{256} a + \frac{801315}{64} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 7 a + 2\) , \( a^{3} - 2 a^{2} - 4 a\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( 4 a^{3} - 7 a^{2} - 9 a + 4\) , \( -202 a^{3} + 710 a^{2} + 186 a - 279\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){x}{y}+\left(a^{3}-3a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a\right){x}^{2}+\left(4a^{3}-7a^{2}-9a+4\right){x}-202a^{3}+710a^{2}+186a-279$ |
| 16.1-h1 |
16.1-h |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$496.7069065$ |
0.968241423 |
\( 12288 a^{2} + 8192 a - 8192 \) |
\( \bigl[0\) , \( a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 4 a^{3} - 14 a^{2} + 7\) , \( 10 a^{3} - 34 a^{2} - 9 a + 12\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4a^{3}-14a^{2}+7\right){x}+10a^{3}-34a^{2}-9a+12$ |
| 16.1-h2 |
16.1-h |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1986.827626$ |
0.968241423 |
\( -16800495556 a^{3} + 24508705228 a^{2} + 114016509456 a + 61852179108 \) |
\( \bigl[a\) , \( -2 a^{3} + 5 a^{2} + 7 a\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 28 a^{3} - 37 a^{2} - 200 a - 116\) , \( -136 a^{3} + 200 a^{2} + 919 a + 494\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a\right){x}^{2}+\left(28a^{3}-37a^{2}-200a-116\right){x}-136a^{3}+200a^{2}+919a+494$ |
| 16.1-h3 |
16.1-h |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$993.4138130$ |
0.968241423 |
\( 18251776 a^{3} - 49274848 a^{2} - 75104256 a + 52712176 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -1\) , \( 0\) , \( a^{3} - 3 a^{2} - 4 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+2\right){x}{y}={x}^{3}-{x}^{2}+\left(a^{3}-3a^{2}-4a+3\right){x}$ |
| 16.1-h4 |
16.1-h |
$4$ |
$4$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.20728$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$124.1767266$ |
0.968241423 |
\( 1371554665152452 a^{3} - 3698538392272844 a^{2} - 5652915138723344 a + 3937837510673452 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 7 a + 2\) , \( -2 a^{3} + 5 a^{2} + 9 a\) , \( 0\) , \( 10 a^{3} - 3 a^{2} - 82 a - 53\) , \( 35 a^{3} - 33 a^{2} - 239 a - 139\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){x}{y}={x}^{3}+\left(-2a^{3}+5a^{2}+9a\right){x}^{2}+\left(10a^{3}-3a^{2}-82a-53\right){x}+35a^{3}-33a^{2}-239a-139$ |
| 20.2-a1 |
20.2-a |
$2$ |
$2$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.060644534$ |
$1230.547176$ |
3.491279670 |
\( -\frac{112390144}{625} a^{3} + \frac{388993024}{625} a^{2} + \frac{105873408}{625} a - \frac{153034752}{625} \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a + 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( a^{3} - 5 a^{2} + 6 a + 7\) , \( -3 a^{3} + 7 a^{2} + 10 a - 1\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-7a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a+1\right){x}^{2}+\left(a^{3}-5a^{2}+6a+7\right){x}-3a^{3}+7a^{2}+10a-1$ |
| 20.2-a2 |
20.2-a |
$2$ |
$2$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{8} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.121289069$ |
$615.2735880$ |
3.491279670 |
\( \frac{20900760736}{390625} a^{3} - \frac{56457895456}{390625} a^{2} - \frac{85761730752}{390625} a + \frac{60542074288}{390625} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -a^{3} + 3 a^{2} + 4 a - 3\) , \( 0\) , \( a^{3} + 11 a^{2} + 8 a - 5\) , \( 9 a^{3} + 12 a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+2\right){x}{y}={x}^{3}+\left(-a^{3}+3a^{2}+4a-3\right){x}^{2}+\left(a^{3}+11a^{2}+8a-5\right){x}+9a^{3}+12a^{2}-4a-2$ |
| 20.2-b1 |
20.2-b |
$4$ |
$6$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.369232431$ |
$615.7619781$ |
3.545570754 |
\( \frac{10326016}{625} a^{3} + \frac{3313664}{625} a^{2} - \frac{35315712}{625} a - \frac{25321472}{625} \) |
\( \bigl[0\) , \( 2 a^{3} - 5 a^{2} - 7 a + 1\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( a^{3} - 4 a^{2} + 2 a + 5\) , \( -3 a^{3} + 11 a^{2} + 2 a - 6\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-7a+1\right){x}^{2}+\left(a^{3}-4a^{2}+2a+5\right){x}-3a^{3}+11a^{2}+2a-6$ |
| 20.2-b2 |
20.2-b |
$4$ |
$6$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1.107697295$ |
$68.41799757$ |
3.545570754 |
\( -\frac{6892680112827387904}{244140625} a^{3} + \frac{18595123571034025984}{244140625} a^{2} + \frac{28373915238881353728}{244140625} a - \frac{19773113142805880832}{244140625} \) |
\( \bigl[0\) , \( 2 a^{3} - 5 a^{2} - 7 a + 1\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 131 a^{3} - 474 a^{2} - 38 a + 145\) , \( 1917 a^{3} - 6578 a^{2} - 2042 a + 2736\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-7a+1\right){x}^{2}+\left(131a^{3}-474a^{2}-38a+145\right){x}+1917a^{3}-6578a^{2}-2042a+2736$ |
| 20.2-b3 |
20.2-b |
$4$ |
$6$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$2.215394591$ |
$34.20899878$ |
3.545570754 |
\( \frac{50846961819776554405396064}{15625} a^{3} - \frac{137114068581410588673397344}{15625} a^{2} - \frac{209567702645805102627646848}{15625} a + \frac{145985485409266205310600112}{15625} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( a^{3} - 2 a^{2} - 6 a\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( 12 a^{3} - 5 a^{2} - 104 a - 116\) , \( 69 a^{3} - 122 a^{2} - 424 a - 177\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+2\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-6a\right){x}^{2}+\left(12a^{3}-5a^{2}-104a-116\right){x}+69a^{3}-122a^{2}-424a-177$ |
| 20.2-b4 |
20.2-b |
$4$ |
$6$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.738464863$ |
$307.8809890$ |
3.545570754 |
\( -\frac{14860902496}{25} a^{3} + \frac{21477579616}{25} a^{2} + \frac{101304729472}{25} a + \frac{55716371632}{25} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( a^{3} - 2 a^{2} - 6 a\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( 22 a^{3} - 35 a^{2} - 144 a - 66\) , \( 87 a^{3} - 130 a^{2} - 584 a - 303\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-8a+2\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-6a\right){x}^{2}+\left(22a^{3}-35a^{2}-144a-66\right){x}+87a^{3}-130a^{2}-584a-303$ |
| 20.2-c1 |
20.2-c |
$4$ |
$6$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.342699464$ |
$9.958892659$ |
3.274489379 |
\( -\frac{6892680112827387904}{244140625} a^{3} + \frac{18595123571034025984}{244140625} a^{2} + \frac{28373915238881353728}{244140625} a - \frac{19773113142805880832}{244140625} \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - 4 a - 1\) , \( a\) , \( -253 a^{3} + 679 a^{2} + 1052 a - 709\) , \( -3132 a^{3} + 8446 a^{2} + 12908 a - 8995\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a-1\right){x}^{2}+\left(-253a^{3}+679a^{2}+1052a-709\right){x}-3132a^{3}+8446a^{2}+12908a-8995$ |
| 20.2-c2 |
20.2-c |
$4$ |
$6$ |
4.4.16448.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$16.66571$ |
$(a), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.780899821$ |
$806.6703054$ |
3.274489379 |
\( \frac{10326016}{625} a^{3} + \frac{3313664}{625} a^{2} - \frac{35315712}{625} a - \frac{25321472}{625} \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - 4 a - 1\) , \( a\) , \( -3 a^{3} + 9 a^{2} + 12 a - 9\) , \( -6 a^{3} + 15 a^{2} + 28 a - 11\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a-1\right){x}^{2}+\left(-3a^{3}+9a^{2}+12a-9\right){x}-6a^{3}+15a^{2}+28a-11$ |
*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.
