| 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 |
| 6500.6-b1 |
6500.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{7} \cdot 13^{2} \) |
$1.60471$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.047842369$ |
$2.215707936$ |
2.544113213 |
\( \frac{22196836}{105625} a + \frac{124665848}{105625} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -4 i + 8\) , \( 8 i - 6\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-4i+8\right){x}+8i-6$ |
| 26000.6-d1 |
26000.6-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{13} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.990894712$ |
1.981789425 |
\( \frac{22196836}{105625} a + \frac{124665848}{105625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 40 i - 9\) , \( 33 i - 73\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(40i-9\right){x}+33i-73$ |
| 32500.6-a1 |
32500.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32500.6 |
\( 2^{2} \cdot 5^{4} \cdot 13 \) |
\( 2^{8} \cdot 5^{19} \cdot 13^{2} \) |
$2.39960$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.011660676$ |
$0.443141587$ |
3.586471342 |
\( \frac{22196836}{105625} a + \frac{124665848}{105625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -93 i + 194\) , \( -617 i + 453\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-93i+194\right){x}-617i+453$ |
| 84500.9-c1 |
84500.9-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{13} \cdot 13^{8} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.719819161$ |
$0.274824745$ |
4.747778834 |
\( \frac{22196836}{105625} a + \frac{124665848}{105625} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 107 i - 547\) , \( -2908 i - 1867\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(107i-547\right){x}-2908i-1867$ |
*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.
