| 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 |
| 20.4-a1 |
20.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{17} \cdot 5^{2} \) |
$1.05215$ |
$(2,a), (2,a+1), (5,a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1.389161942$ |
$7.344894602$ |
0.814469976 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}-a$ |
| 100.6-a1 |
100.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
100.6 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{17} \cdot 5^{8} \) |
$1.57333$ |
$(2,a), (2,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.284736723$ |
2.359824525 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -27\) , \( -9 a - 26\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2-27{x}-9a-26$ |
| 500.6-d1 |
500.6-d |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
500.6 |
\( 2^{2} \cdot 5^{3} \) |
\( 2^{5} \cdot 5^{8} \) |
$2.35267$ |
$(2,a), (2,a+1), (5,a+1), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.269898484$ |
$3.284736723$ |
3.821478377 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 2 a - 1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(2a-1\right){x}-a$ |
| 640.14-d1 |
640.14-d |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
640.14 |
\( 2^{7} \cdot 5 \) |
\( 2^{35} \cdot 5^{2} \) |
$2.50244$ |
$(2,a), (2,a+1), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.799890181$ |
$2.596812390$ |
2.984558394 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -8 a + 34\) , \( -5 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-8a+34\right){x}-5a-20$ |
| 640.4-c1 |
640.4-c |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
640.4 |
\( 2^{7} \cdot 5 \) |
\( 2^{35} \cdot 5^{2} \) |
$2.50244$ |
$(2,a), (2,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.596812390$ |
1.865605094 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a + 20\) , \( -4 a + 48\bigr] \) |
${y}^2={x}^3-a{x}^2+\left(-12a+20\right){x}-4a+48$ |
| 1280.10-f1 |
1280.10-f |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
1280.10 |
\( 2^{8} \cdot 5 \) |
\( 2^{41} \cdot 5^{2} \) |
$2.97592$ |
$(2,a), (2,a+1), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.827336183$ |
$1.836223650$ |
4.365628051 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 19 a - 64\) , \( -65 a + 124\bigr] \) |
${y}^2={x}^3+{x}^2+\left(19a-64\right){x}-65a+124$ |
| 1620.4-b1 |
1620.4-b |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
1620.4 |
\( 2^{2} \cdot 3^{4} \cdot 5 \) |
\( 2^{17} \cdot 3^{12} \cdot 5^{2} \) |
$3.15644$ |
$(2,a), (2,a+1), (5,a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.448298200$ |
5.276728053 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 9 a - 34\) , \( -40 a + 51\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(9a-34\right){x}-40a+51$ |
| 2500.8-l1 |
2500.8-l |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
2500.8 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{17} \cdot 5^{14} \) |
$3.51807$ |
$(2,a), (2,a+1), (5,a+1), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.997365599$ |
$1.468978920$ |
12.63078489 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 27 a - 96\) , \( 94 a - 249\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(27a-96\right){x}+94a-249$ |
| 3200.21-c1 |
3200.21-c |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
3200.21 |
\( 2^{7} \cdot 5^{2} \) |
\( 2^{35} \cdot 5^{8} \) |
$3.74203$ |
$(2,a), (2,a+1), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.161329805$ |
1.668647924 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a + 176\) , \( -364 a + 492\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(16a+176\right){x}-364a+492$ |
| 3200.6-c1 |
3200.6-c |
$4$ |
$6$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
3200.6 |
\( 2^{7} \cdot 5^{2} \) |
\( 2^{35} \cdot 5^{8} \) |
$3.74203$ |
$(2,a), (2,a+1), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.606873886$ |
$1.161329805$ |
2.025317702 |
\( \frac{240871}{200} a + \frac{507813}{100} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -32 a + 187\) , \( 229 a + 291\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-32a+187\right){x}+229a+291$ |
*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.
