| 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 |
| 1922.1-a1 |
1922.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{8} \cdot 31^{2} \) |
$2.04959$ |
$(a+1), (31)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$19.66889363$ |
2.838960258 |
\( -\frac{35937}{496} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}+1$ |
| 1922.1-a2 |
1922.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{2} \cdot 31^{8} \) |
$2.04959$ |
$(a+1), (31)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.917223407$ |
2.838960258 |
\( \frac{3196010817}{1847042} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$ |
| 1922.1-a3 |
1922.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{4} \cdot 31^{4} \) |
$2.04959$ |
$(a+1), (31)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$19.66889363$ |
2.838960258 |
\( \frac{979146657}{3844} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -21\) , \( 41\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-21{x}+41$ |
| 1922.1-a4 |
1922.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{2} \cdot 31^{2} \) |
$2.04959$ |
$(a+1), (31)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$19.66889363$ |
2.838960258 |
\( \frac{3999236143617}{62} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -331\) , \( 2397\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-331{x}+2397$ |
| 1922.1-b1 |
1922.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{8} \cdot 31^{2} \) |
$2.04959$ |
$(a+1), (31)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.604379946$ |
$5.013606122$ |
2.322024586 |
\( -\frac{35937}{496} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-2{x}-2$ |
| 1922.1-b2 |
1922.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{2} \cdot 31^{8} \) |
$2.04959$ |
$(a+1), (31)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.604379946$ |
$5.013606122$ |
2.322024586 |
\( \frac{3196010817}{1847042} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -32\) , \( -6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-32{x}-6$ |
| 1922.1-b3 |
1922.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{4} \cdot 31^{4} \) |
$2.04959$ |
$(a+1), (31)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.208759892$ |
$5.013606122$ |
2.322024586 |
\( \frac{979146657}{3844} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -22\) , \( -42\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-22{x}-42$ |
| 1922.1-b4 |
1922.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{2} \cdot 31^{2} \) |
$2.04959$ |
$(a+1), (31)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.417519785$ |
$1.253401530$ |
2.322024586 |
\( \frac{3999236143617}{62} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -332\) , \( -2398\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-332{x}-2398$ |
*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.
