| 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-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 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 1\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a+1\right){x}-3a+3$ |
| 2304.2-a1 |
2304.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.055055708$ |
1.842267908 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -a + 1\) , \( 3 a - 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-a+1\right){x}+3a-3$ |
| 5184.3-e1 |
5184.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5184.3 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$2.51479$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.018351902$ |
1.228178605 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 6\) , \( 72 a - 74\bigr] \) |
${y}^2={x}^{3}+\left(-9a+6\right){x}+72a-74$ |
| 6912.2-g1 |
6912.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.499008604$ |
$1.763837235$ |
2.123049817 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a\) , \( -9 a + 27\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+3a{x}-9a+27$ |
| 6912.2-p1 |
6912.2-p |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.157955638$ |
$1.763837235$ |
4.032167232 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a\) , \( 9 a - 27\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+3a{x}+9a-27$ |
| 6912.3-i1 |
6912.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.763837235$ |
2.127267746 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 5\) , \( -15 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-5\right){x}-15a-3$ |
| 6912.3-q1 |
6912.3-q |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{10} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.763837235$ |
4.254535492 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 5\) , \( 15 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-5\right){x}+15a+3$ |
| 14400.4-i1 |
14400.4-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.4 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{6} \) |
$3.24658$ |
$(-a), (a-1), (-a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.366262447$ |
0.823887255 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 33 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+7\right){x}+33a+3$ |
| 14400.6-h1 |
14400.6-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.6 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{6} \) |
$3.24658$ |
$(-a), (a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.366262447$ |
2.471661766 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 9\) , \( 21 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-9\right){x}+21a-48$ |
| 20736.3-m1 |
20736.3-m |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.160122483$ |
$1.018351902$ |
6.293088271 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 6\) , \( -72 a + 74\bigr] \) |
${y}^2={x}^{3}+\left(-9a+6\right){x}-72a+74$ |
| 36864.2-e1 |
36864.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{4} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.528167139$ |
$1.527527854$ |
2.815293279 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 3\) , \( -20 a + 21\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a+3\right){x}-20a+21$ |
| 36864.2-bm1 |
36864.2-bm |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{4} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.972594271$ |
$1.527527854$ |
5.375337641 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a + 3\) , \( 20 a - 21\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4a+3\right){x}+20a-21$ |
*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.
