| 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 |
| 10400.3-d5 |
10400.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10400.3 |
\( 2^{5} \cdot 5^{2} \cdot 13 \) |
\( 2^{6} \cdot 5^{12} \cdot 13^{2} \) |
$1.80479$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.190165251$ |
2.380330502 |
\( -\frac{246826028856}{66015625} a + \frac{291128921792}{66015625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -23 i - 38\) , \( 61 i + 96\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-23i-38\right){x}+61i+96$ |
| 52000.3-d5 |
52000.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.3 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{18} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.841594023$ |
$0.532258081$ |
3.920813205 |
\( -\frac{246826028856}{66015625} a + \frac{291128921792}{66015625} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 218 i + 28\) , \( 512 i + 961\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(218i+28\right){x}+512i+961$ |
| 52000.5-b5 |
52000.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.5 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{18} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.621322125$ |
$0.532258081$ |
3.451847214 |
\( -\frac{246826028856}{66015625} a + \frac{291128921792}{66015625} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -88 i + 201\) , \( -755 i - 644\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-88i+201\right){x}-755i-644$ |
| 83200.3-c5 |
83200.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.3 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{18} \cdot 5^{12} \cdot 13^{2} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.595082625$ |
1.190165251 |
\( -\frac{246826028856}{66015625} a + \frac{291128921792}{66015625} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -86 i - 153\) , \( -405 i - 615\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-86i-153\right){x}-405i-615$ |
*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.
