| 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 |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.700238080$ |
$13.75037163$ |
3.230860926 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$7.400476160$ |
$27.50074327$ |
3.230860926 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1008 a - 7937\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(1008a-7937\right){x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.700238080$ |
$13.75037163$ |
3.230860926 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 57\) , \( 134\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+57{x}+134$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.700238080$ |
$55.00148654$ |
3.230860926 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 88\) , \( 153\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+88{x}+153$ |
| 32.1-b1 |
32.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.314214059$ |
$27.50074327$ |
5.787608512 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a - 63\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(8a-63\right){x}$ |
| 32.1-b2 |
32.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$6.628428118$ |
$13.75037163$ |
5.787608512 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a + 63\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(8a+63\right){x}$ |
| 32.1-c1 |
32.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.314214059$ |
$27.50074327$ |
5.787608512 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a - 63\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-8a-63\right){x}$ |
| 32.1-c2 |
32.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$6.628428118$ |
$13.75037163$ |
5.787608512 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 63\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-8a+63\right){x}$ |
| 32.1-d1 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$10.79897868$ |
$27.50074327$ |
4.714561267 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-d2 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$21.59795736$ |
$13.75037163$ |
4.714561267 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1008 a + 7937\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-1008a+7937\right){x}$ |
| 32.1-d3 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$5.399489341$ |
$13.75037163$ |
4.714561267 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 2772 a - 21736\) , \( 237496 a - 1869879\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(2772a-21736\right){x}+237496a-1869879$ |
| 32.1-d4 |
32.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$5.399489341$ |
$55.00148654$ |
4.714561267 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 2772 a - 21767\) , \( -207004 a + 1630102\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(2772a-21767\right){x}-207004a+1630102$ |
*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.
