| 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 |
| 3072.1-b1 |
3072.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.208930895$ |
$2.876942816$ |
1.388139971 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 1\) , \( 15 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-1\right){x}+15a-9$ |
| 3072.1-e1 |
3072.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.15227$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.876942816$ |
1.661003709 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 10\) , \( -15 a + 9\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a-10\right){x}-15a+9$ |
| 9216.1-c1 |
9216.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.51647$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.287659545$ |
$1.661003709$ |
2.206880166 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 29\) , \( 23 a - 92\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a+29\right){x}+23a-92$ |
| 9216.1-e1 |
9216.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.51647$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.661003709$ |
1.917961877 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 32\) , \( -20 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-32\right){x}-20a+60$ |
| 12288.1-c2 |
12288.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 43\) , \( -116 a + 29\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a+43\right){x}-116a+29$ |
| 12288.1-f2 |
12288.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12288.1 |
\( 2^{12} \cdot 3 \) |
\( 2^{30} \cdot 3^{4} \) |
$1.62956$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.438471408$ |
1.661003709 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -39 a - 4\) , \( 116 a - 29\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-39a-4\right){x}+116a-29$ |
| 36864.1-i2 |
36864.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.384142245$ |
$0.830501854$ |
2.947080732 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 13 a - 128\) , \( 58 a - 621\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-128\right){x}+58a-621$ |
| 36864.1-q2 |
36864.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{10} \) |
$2.14462$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.830501854$ |
1.917961877 |
\( -\frac{188632}{9} a - 7424 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 13 a - 128\) , \( -58 a + 621\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a-128\right){x}-58a+621$ |
*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.
