| 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 |
| 32.1-a1 |
32.1-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$314.7722181$ |
1.858948680 |
\( 43136 a^{2} - 68416 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + 4 a\) , \( 0\) , \( 12 a^{3} - 28 a^{2} - 16 a + 51\) , \( 65 a^{3} - 139 a^{2} - 100 a + 223\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(12a^{3}-28a^{2}-16a+51\right){x}+65a^{3}-139a^{2}-100a+223$ |
| 32.1-a2 |
32.1-a |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$314.7722181$ |
1.858948680 |
\( -43136 a^{2} + 190400 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a^{3} + a^{2} - a - 2\) , \( 16 a^{3} - 32 a^{2} - 24 a + 49\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(a^{3}+a^{2}-a-2\right){x}+16a^{3}-32a^{2}-24a+49$ |
| 32.1-b1 |
32.1-b |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.048120886$ |
$1092.508130$ |
2.483815271 |
\( 43136 a^{2} - 68416 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( 13 a^{3} - 24 a^{2} - 21 a + 39\) , \( -79 a^{3} + 168 a^{2} + 125 a - 266\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(13a^{3}-24a^{2}-21a+39\right){x}-79a^{3}+168a^{2}+125a-266$ |
| 32.1-b2 |
32.1-b |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.096241773$ |
$1092.508130$ |
2.483815271 |
\( -43136 a^{2} + 190400 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + 4 a\) , \( 0\) , \( -3 a^{2} + 4 a + 10\) , \( -17 a^{3} + 34 a^{2} + 28 a - 49\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-3a^{2}+4a+10\right){x}-17a^{3}+34a^{2}+28a-49$ |
| 32.1-c1 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.490272341$ |
$378.1454402$ |
2.189763753 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - a - 2\) , \( 0\) , \( 9 a^{3} + 21 a^{2} - 15 a - 32\) , \( 15 a^{3} + 33 a^{2} - 24 a - 52\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(9a^{3}+21a^{2}-15a-32\right){x}+15a^{3}+33a^{2}-24a-52$ |
| 32.1-c2 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.980544682$ |
$1512.581761$ |
2.189763753 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -9 a^{3} + 14 a^{2} + 37 a - 60\) , \( -3 a^{3} + 4 a^{2} + 11 a - 18\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-9a^{3}+14a^{2}+37a-60\right){x}-3a^{3}+4a^{2}+11a-18$ |
| 32.1-c3 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.961089364$ |
$189.0727201$ |
2.189763753 |
\( 287496 \) |
\( \bigl[a^{2} - 3\) , \( 1\) , \( 0\) , \( -2\) , \( -3\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+{x}^{2}-2{x}-3$ |
| 32.1-c4 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.490272341$ |
$3025.163522$ |
2.189763753 |
\( 287496 \) |
\( \bigl[a^{2} - 3\) , \( 1\) , \( a^{2} - 3\) , \( -3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}-3{x}$ |
| 32.1-c5 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.922178729$ |
$23.63409001$ |
2.189763753 |
\( 29071392966 a^{2} - 46101020778 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 5 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -25 a^{3} - 8 a^{2} + 77 a - 34\) , \( -337 a^{3} + 214 a^{2} + 1303 a - 1333\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-25a^{3}-8a^{2}+77a-34\right){x}-337a^{3}+214a^{2}+1303a-1333$ |
| 32.1-c6 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.922178729$ |
$23.63409001$ |
2.189763753 |
\( -29071392966 a^{2} + 128327337018 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - 4 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -23 a^{3} - 14 a^{2} + 63 a - 19\) , \( -372 a^{3} - 546 a^{2} + 787 a + 613\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-23a^{3}-14a^{2}+63a-19\right){x}-372a^{3}-546a^{2}+787a+613$ |
| 32.1-c7 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.245136170$ |
$1512.581761$ |
2.189763753 |
\( -29071392966 a^{2} + 128327337018 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 5 a\) , \( a^{2} + a - 2\) , \( -25 a^{3} - 15 a^{2} + 71 a - 16\) , \( 299 a^{3} + 550 a^{2} - 537 a - 783\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-25a^{3}-15a^{2}+71a-16\right){x}+299a^{3}+550a^{2}-537a-783$ |
| 32.1-c8 |
32.1-c |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.245136170$ |
$1512.581761$ |
2.189763753 |
\( 29071392966 a^{2} - 46101020778 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - 4 a\) , \( a^{3} - 3 a\) , \( -23 a^{3} - 7 a^{2} + 69 a - 37\) , \( 259 a^{3} - 191 a^{2} - 1019 a + 1102\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-23a^{3}-7a^{2}+69a-37\right){x}+259a^{3}-191a^{2}-1019a+1102$ |
| 32.1-d1 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$378.1454402$ |
2.233211594 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - a - 2\) , \( 0\) , \( 5 a^{3} - 3 a^{2} - 23 a + 24\) , \( a^{3} + a^{2} - 6 a + 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(5a^{3}-3a^{2}-23a+24\right){x}+a^{3}+a^{2}-6a+4$ |
| 32.1-d2 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1512.581761$ |
2.233211594 |
\( 1728 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - a - 2\) , \( 0\) , \( -3 a^{3} + 2 a^{2} + 9 a - 9\) , \( -3 a^{3} - 3 a^{2} + 6 a + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-3a^{3}+2a^{2}+9a-9\right){x}-3a^{3}-3a^{2}+6a+3$ |
| 32.1-d3 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$94.53636006$ |
2.233211594 |
\( -29071392966 a^{2} + 128327337018 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( 79 a^{3} - 162 a^{2} - 130 a + 250\) , \( -4247 a^{3} + 8938 a^{2} + 6721 a - 14192\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(79a^{3}-162a^{2}-130a+250\right){x}-4247a^{3}+8938a^{2}+6721a-14192$ |
| 32.1-d4 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$378.1454402$ |
2.233211594 |
\( 29071392966 a^{2} - 46101020778 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} - 5 a\) , \( a^{3} - 4 a + 1\) , \( 7 a^{3} - 24 a^{2} + 10 a + 18\) , \( -190 a^{3} + 298 a^{2} + 645 a - 909\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(7a^{3}-24a^{2}+10a+18\right){x}-190a^{3}+298a^{2}+645a-909$ |
| 32.1-d5 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$756.2908805$ |
2.233211594 |
\( 287496 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 3\) , \( a^{3} - 3 a\) , \( -5 a^{2} + 6\) , \( 2 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-5a^{2}+6\right){x}+2a^{2}-4$ |
| 32.1-d6 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$756.2908805$ |
2.233211594 |
\( 287496 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - 3\) , \( 0\) , \( -4 a^{2} + 6\) , \( -15 a^{2} + 24\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4a^{2}+6\right){x}-15a^{2}+24$ |
| 32.1-d7 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$94.53636006$ |
2.233211594 |
\( 29071392966 a^{2} - 46101020778 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} - 4 a\) , \( a + 1\) , \( 8 a^{3} - 25 a^{2} + 5 a + 21\) , \( 161 a^{3} - 263 a^{2} - 513 a + 740\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(8a^{3}-25a^{2}+5a+21\right){x}+161a^{3}-263a^{2}-513a+740$ |
| 32.1-d8 |
32.1-d |
$8$ |
$16$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$378.1454402$ |
2.233211594 |
\( -29071392966 a^{2} + 128327337018 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 81 a^{3} - 159 a^{2} - 133 a + 242\) , \( 4166 a^{3} - 8750 a^{2} - 6605 a + 13876\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(81a^{3}-159a^{2}-133a+242\right){x}+4166a^{3}-8750a^{2}-6605a+13876$ |
| 32.1-e1 |
32.1-e |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.096241773$ |
$1092.508130$ |
2.483815271 |
\( -43136 a^{2} + 190400 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 3 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 5 a - 5\) , \( 16 a^{3} + 33 a^{2} - 26 a - 53\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(a^{3}+a^{2}-5a-5\right){x}+16a^{3}+33a^{2}-26a-53$ |
| 32.1-e2 |
32.1-e |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.048120886$ |
$1092.508130$ |
2.483815271 |
\( 43136 a^{2} - 68416 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - 2 a^{2} + a + 2\) , \( -13 a^{3} - 17 a^{2} + 57 a + 74\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-a^{3}-2a^{2}+a+2\right){x}-13a^{3}-17a^{2}+57a+74$ |
| 32.1-f1 |
32.1-f |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$314.7722181$ |
1.858948680 |
\( 43136 a^{2} - 68416 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 5 a - 1\) , \( 0\) , \( a^{3} - 5 a - 1\) , \( 13 a^{3} + 16 a^{2} - 59 a - 74\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(a^{3}-5a-1\right){x}+13a^{3}+16a^{2}-59a-74$ |
| 32.1-f2 |
32.1-f |
$2$ |
$2$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$11.66759$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$314.7722181$ |
1.858948680 |
\( -43136 a^{2} + 190400 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -2 a^{3} - 5 a^{2} + 4 a + 11\) , \( -18 a^{3} - 38 a^{2} + 28 a + 59\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-2a^{3}-5a^{2}+4a+11\right){x}-18a^{3}-38a^{2}+28a+59$ |
*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.
