| 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 |
| 8450.6-a1 |
8450.6-a |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.6 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{3} \cdot 5^{9} \cdot 13^{4} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.129578811$ |
$1.219656637$ |
1.896499887 |
\( \frac{2412409957}{62500} a - \frac{352209201}{62500} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -25 i + 57\) , \( 144 i + 130\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-25i+57\right){x}+144i+130$ |
| 42250.6-g1 |
42250.6-g |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{3} \cdot 5^{15} \cdot 13^{10} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.151279787$ |
3.630714895 |
\( \frac{2412409957}{62500} a - \frac{352209201}{62500} \) |
\( \bigl[i\) , \( i\) , \( i\) , \( -3988 i + 464\) , \( -54183 i + 82950\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-3988i+464\right){x}-54183i+82950$ |
| 42250.9-c1 |
42250.9-c |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.9 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{3} \cdot 5^{15} \cdot 13^{10} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.151279787$ |
0.907678723 |
\( \frac{2412409957}{62500} a - \frac{352209201}{62500} \) |
\( \bigl[1\) , \( -i + 1\) , \( i\) , \( 670 i - 3958\) , \( 24026 i - 97102\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(670i-3958\right){x}+24026i-97102$ |
| 67600.6-e1 |
67600.6-e |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{15} \cdot 5^{9} \cdot 13^{10} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.169135944$ |
2.029631328 |
\( \frac{2412409957}{62500} a - \frac{352209201}{62500} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -2213 i - 2330\) , \( -64914 i - 26153\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-2213i-2330\right){x}-64914i-26153$ |
*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.
