| 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 |
| 3250.6-a2 |
3250.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3250.6 |
\( 2 \cdot 5^{3} \cdot 13 \) |
\( 2^{4} \cdot 5^{7} \cdot 13 \) |
$1.34940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.057234923$ |
$3.416837829$ |
1.564499601 |
\( -\frac{5423261}{8125} a - \frac{19770367}{32500} \) |
\( \bigl[i\) , \( i\) , \( i + 1\) , \( -i - 3\) , \( -2 i + 4\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i-3\right){x}-2i+4$ |
| 16250.6-g2 |
16250.6-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{4} \cdot 5^{19} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.683367565$ |
2.733470263 |
\( -\frac{5423261}{8125} a - \frac{19770367}{32500} \) |
\( \bigl[1\) , \( i + 1\) , \( i + 1\) , \( -8 i - 80\) , \( 24 i - 480\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-8i-80\right){x}+24i-480$ |
| 26000.6-c2 |
26000.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{16} \cdot 5^{13} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.570312646$ |
$0.764028165$ |
3.485879403 |
\( -\frac{5423261}{8125} a - \frac{19770367}{32500} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 47 i - 44\) , \( -330 i - 19\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(47i-44\right){x}-330i-19$ |
| 42250.9-b2 |
42250.9-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.9 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{13} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.423806573$ |
1.695226293 |
\( -\frac{5423261}{8125} a - \frac{19770367}{32500} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( 72 i + 196\) , \( 1808 i - 556\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+\left(72i+196\right){x}+1808i-556$ |
*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.
