| 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 |
| 96100.3-a1 |
96100.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
96100.3 |
\( 2^{2} \cdot 5^{2} \cdot 31^{2} \) |
\( 2^{4} \cdot 5^{20} \cdot 31^{7} \) |
$2.72508$ |
$(6a-5), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.498448154$ |
$0.098366399$ |
3.403986729 |
\( \frac{507226797683}{242187500} a + \frac{309491975847}{605468750} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 5809 a - 1609\) , \( -101245 a - 36864\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5809a-1609\right){x}-101245a-36864$ |
| 96100.3-a2 |
96100.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
96100.3 |
\( 2^{2} \cdot 5^{2} \cdot 31^{2} \) |
\( 2^{8} \cdot 5^{10} \cdot 31^{8} \) |
$2.72508$ |
$(6a-5), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.749224077$ |
$0.196732798$ |
3.403986729 |
\( -\frac{271496126491}{9610000} a + \frac{721597679759}{48050000} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1829 a + 571\) , \( -15105 a + 44100\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1829a+571\right){x}-15105a+44100$ |
| 96100.3-b1 |
96100.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
96100.3 |
\( 2^{2} \cdot 5^{2} \cdot 31^{2} \) |
\( 2^{12} \cdot 5^{2} \cdot 31^{6} \) |
$2.72508$ |
$(6a-5), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.877249340$ |
2.025920571 |
\( -\frac{1860867}{320} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 90 a - 62\) , \( 324 a - 52\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(90a-62\right){x}+324a-52$ |
| 96100.3-b2 |
96100.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
96100.3 |
\( 2^{2} \cdot 5^{2} \cdot 31^{2} \) |
\( 2^{4} \cdot 5^{6} \cdot 31^{6} \) |
$2.72508$ |
$(6a-5), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.877249340$ |
2.025920571 |
\( \frac{804357}{500} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 46 a + 21\) , \( 47 a + 21\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a+21\right){x}+47a+21$ |
| 96100.3-b3 |
96100.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
96100.3 |
\( 2^{2} \cdot 5^{2} \cdot 31^{2} \) |
\( 2^{2} \cdot 5^{12} \cdot 31^{6} \) |
$2.72508$ |
$(6a-5), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{2} \) |
$1$ |
$0.438624670$ |
2.025920571 |
\( \frac{57960603}{31250} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -194 a - 89\) , \( 423 a - 127\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-194a-89\right){x}+423a-127$ |
| 96100.3-b4 |
96100.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
96100.3 |
\( 2^{2} \cdot 5^{2} \cdot 31^{2} \) |
\( 2^{6} \cdot 5^{4} \cdot 31^{6} \) |
$2.72508$ |
$(6a-5), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{2} \) |
$1$ |
$0.438624670$ |
2.025920571 |
\( \frac{8527173507}{200} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1490 a - 1022\) , \( 19076 a - 1708\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1490a-1022\right){x}+19076a-1708$ |
*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.
