| 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 |
| 8450.4-b1 |
8450.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.4 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{27} \cdot 5^{5} \cdot 13^{8} \) |
$1.71349$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.179846587$ |
1.079079527 |
\( -\frac{577233446569}{2048000} a - \frac{853138583973}{2048000} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 936 i - 4280\) , \( -35656 i + 106340\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(936i-4280\right){x}-35656i+106340$ |
| 42250.4-d1 |
42250.4-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.4 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{27} \cdot 5^{11} \cdot 13^{2} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.289993909$ |
1.739963456 |
\( -\frac{577233446569}{2048000} a - \frac{853138583973}{2048000} \) |
\( \bigl[i\) , \( -i - 1\) , \( i\) , \( 1602 i - 525\) , \( 24899 i + 8901\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(1602i-525\right){x}+24899i+8901$ |
| 42250.7-j1 |
42250.7-j |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.7 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{27} \cdot 5^{11} \cdot 13^{2} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$0.048178273$ |
$0.289993909$ |
6.035647390 |
\( -\frac{577233446569}{2048000} a - \frac{853138583973}{2048000} \) |
\( \bigl[i\) , \( -i\) , \( 1\) , \( 56 i + 1684\) , \( 26068 i - 1433\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(56i+1684\right){x}+26068i-1433$ |
| 67600.4-b1 |
67600.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{39} \cdot 5^{5} \cdot 13^{2} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.553427995$ |
$0.324223047$ |
4.029257268 |
\( -\frac{577233446569}{2048000} a - \frac{853138583973}{2048000} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 1105 i + 772\) , \( -1732 i + 18623\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(1105i+772\right){x}-1732i+18623$ |
*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.
