| 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 |
| 576.2-a1 |
576.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.908836754$ |
0.548049183 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+16{x}-180$ |
| 576.2-a2 |
576.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.270694035$ |
0.548049183 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 576.2-a3 |
576.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.635347017$ |
0.548049183 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}+4$ |
| 576.2-a4 |
576.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.817673508$ |
0.548049183 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-24{x}-36$ |
| 576.2-a5 |
576.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.817673508$ |
0.548049183 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+220$ |
| 576.2-a6 |
576.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.908836754$ |
0.548049183 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-384{x}-2772$ |
| 576.2-b1 |
576.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.055055708$ |
2.763401863 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 1\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a+1\right){x}-3a+3$ |
| 576.2-b2 |
576.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{8} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.527527854$ |
2.763401863 |
\( -\frac{18321686}{729} a + \frac{5918108}{243} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 41\) , \( -59 a + 35\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a+41\right){x}-59a+35$ |
| 576.2-c1 |
576.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.055055708$ |
2.763401863 |
\( \frac{868}{27} a - \frac{856}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a\) , \( 3 a\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+a{x}+3a$ |
| 576.2-c2 |
576.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{8} \) |
$1.45191$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.527527854$ |
2.763401863 |
\( \frac{18321686}{729} a - \frac{567362}{729} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a + 40\) , \( 59 a - 24\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a+40\right){x}+59a-24$ |
*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.
