| 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 |
| 5776.1-a1 |
5776.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5776.1 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$1.55803$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.175047917$ |
$3.480133765$ |
2.436760673 |
\( -\frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 2 i + 7\) , \( 5 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(2i+7\right){x}+5i-4$ |
| 9025.1-a1 |
9025.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9025.1 |
\( 5^{2} \cdot 19^{2} \) |
\( 5^{6} \cdot 19^{2} \) |
$1.74193$ |
$(-a-2), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.128343938$ |
$3.112726268$ |
1.597998197 |
\( -\frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[1\) , \( i\) , \( i\) , \( 9 i + 2\) , \( -3 i - 13\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(9i+2\right){x}-3i-13$ |
| 9025.3-b1 |
9025.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9025.3 |
\( 5^{2} \cdot 19^{2} \) |
\( 5^{6} \cdot 19^{2} \) |
$1.74193$ |
$(2a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.282671580$ |
$3.112726268$ |
3.519517013 |
\( -\frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[1\) , \( -i\) , \( 0\) , \( -5 i + 8\) , \( -11 i - 9\bigr] \) |
${y}^2+{x}{y}={x}^{3}-i{x}^{2}+\left(-5i+8\right){x}-11i-9$ |
| 61009.1-a1 |
61009.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61009.1 |
\( 13^{2} \cdot 19^{2} \) |
\( 13^{6} \cdot 19^{2} \) |
$2.80878$ |
$(-3a-2), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.930430882$ |
1.930430882 |
\( -\frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( 18 i - 18\) , \( -45 i + 8\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(18i-18\right){x}-45i+8$ |
| 61009.3-b1 |
61009.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
61009.3 |
\( 13^{2} \cdot 19^{2} \) |
\( 13^{6} \cdot 19^{2} \) |
$2.80878$ |
$(2a+3), (19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.930430882$ |
1.930430882 |
\( -\frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[i\) , \( -i + 1\) , \( 1\) , \( -26 i\) , \( 27 i - 42\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+\left(-i+1\right){x}^{2}-26i{x}+27i-42$ |
| 92416.1-j1 |
92416.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{24} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.720811507$ |
$1.740066882$ |
5.017040932 |
\( -\frac{283645}{19} a + \frac{733644}{19} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 12 i + 28\) , \( -44 i + 32\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(12i+28\right){x}-44i+32$ |
*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.
