| 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 |
| 3250.4-a1 |
3250.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3250.4 |
\( 2 \cdot 5^{3} \cdot 13 \) |
\( 2^{17} \cdot 5^{11} \cdot 13 \) |
$1.34940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$0.939702506$ |
0.939702506 |
\( \frac{19040273}{33280} a - \frac{28339689}{33280} \) |
\( \bigl[i\) , \( i\) , \( i + 1\) , \( 39 i + 19\) , \( -52 i - 186\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(39i+19\right){x}-52i-186$ |
| 16250.6-h1 |
16250.6-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{17} \cdot 5^{11} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 17 \) |
$0.011864458$ |
$0.939702506$ |
4.548817186 |
\( \frac{19040273}{33280} a - \frac{28339689}{33280} \) |
\( \bigl[1\) , \( -i + 1\) , \( 0\) , \( -30 i + 33\) , \( 88 i + 145\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-30i+33\right){x}+88i+145$ |
| 26000.4-i1 |
26000.4-i |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{29} \cdot 5^{5} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.050619341$ |
2.101238683 |
\( \frac{19040273}{33280} a - \frac{28339689}{33280} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 8 i + 34\) , \( -94 i + 68\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(8i+34\right){x}-94i+68$ |
| 42250.6-h1 |
42250.6-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{17} \cdot 5^{5} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 17 \) |
$0.074824229$ |
$0.582778755$ |
5.930412106 |
\( \frac{19040273}{33280} a - \frac{28339689}{33280} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -112 i - 22\) , \( 576 i - 476\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-112i-22\right){x}+576i-476$ |
*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.
