| 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 |
| 1024.6-a3 |
1024.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.33740$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.494440753$ |
$3.437592909$ |
1.941708926 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^{3}-11{x}-14$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.59045$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.494440753$ |
$6.875185818$ |
2.745991098 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+4{x}-1$ |
| 64.1-b3 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \cdot 5^{12} \) |
$2.31645$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1.494440753$ |
$6.875185818$ |
4.484184685 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 4 a + 53\) , \( 20 a - 387\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(4a+53\right){x}+20a-387$ |
| 32.1-d3 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-42}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 3^{12} \) |
$2.75474$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.655997444$ |
$6.875185818$ |
5.635305225 |
\( 287496 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 33\) , \( 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+33{x}+7$ |
| 32.1-c4 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-70}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 5^{12} \) |
$3.55635$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1.494440753$ |
$6.875185818$ |
4.912178208 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 22\) , \( -7\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+22{x}-7$ |
| 64.1-b4 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-77}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \cdot 37^{12} \) |
$4.43567$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1.494440753$ |
$6.875185818$ |
2.341789076 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 411 a + 97\) , \( -9515 a - 80503\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(411a+97\right){x}-9515a-80503$ |
| 64.1-a3 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-133}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \cdot 13^{12} \) |
$5.82961$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1.494440753$ |
$13.75037163$ |
1.781834313 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -a + 596\) , \( -109 a - 1518\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-a+596\right){x}-109a-1518$ |
| 32.1-c4 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-154}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 11^{12} \) |
$5.27493$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$12.71214635$ |
$13.75037163$ |
14.08552244 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 136\) , \( -123\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+136{x}-123$ |
| 64.1-b3 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-161}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \cdot 43^{12} \) |
$6.41396$ |
$(2,a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$7.747090612$ |
$13.75037163$ |
16.79075131 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -370 a + 3351\) , \( 4658 a - 149669\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-370a+3351\right){x}+4658a-149669$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 13^{12} \) |
$5.73445$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1.494440753$ |
$13.75037163$ |
3.046403601 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 256\) , \( -365\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+256{x}-365$ |
| 32.1-e4 |
32.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 29^{12} \) |
$6.15979$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$4.029713766$ |
$13.75037163$ |
15.29463013 |
\( 287496 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 11 a + 3226\) , \( -3122 a - 41328\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(11a+3226\right){x}-3122a-41328$ |
| 64.1-a3 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-217}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \cdot 19^{12} \) |
$7.44635$ |
$(2,a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$5.529786585$ |
$13.75037163$ |
10.32340428 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 11 a + 1118\) , \( -253 a - 2976\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(11a+1118\right){x}-253a-2976$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-238}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \cdot 17^{12} \) |
$6.55759$ |
$(2,a)$ |
$3$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$10.61004393$ |
$13.75037163$ |
18.91355363 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 346\) , \( -515\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+346{x}-515$ |
| 1024.1-m3 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$2.31645$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.494440753$ |
$27.50074327$ |
4.484184685 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 55 a - 154\) , \( -336 a + 938\bigr] \) |
${y}^2={x}^{3}+\left(55a-154\right){x}-336a+938$ |
| 64.1-b4 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$1.33740$ |
$(a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.494440753$ |
$55.00148654$ |
1.941708926 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 135 a - 341\) , \( -1379 a + 3661\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(135a-341\right){x}-1379a+3661$ |
| 32.1-e4 |
32.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.59045$ |
$(-a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.494440753$ |
$55.00148654$ |
2.745991098 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 4\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+4{x}+1$ |
| 32.1-d4 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$2.75474$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.663999361$ |
$55.00148654$ |
5.635305225 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 572 a - 3707\) , \( -18900 a + 122486\bigr] \) |
${y}^2={x}^{3}+\left(572a-3707\right){x}-18900a+122486$ |
| 64.1-f6 |
64.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$16.83174$ |
$(1/3a^3+a^2-2/3a-2)$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.398664646$ |
$3025.163522$ |
5.384043506 |
\( 287496 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a\) , \( -3\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a\right){y}={x}^{3}+{x}^{2}-3{x}$ |
*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.
