| 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 |
| 3136.2-b1 |
3136.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3136.2 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.15823$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.197869643$ |
1.846290899 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-4$ |
| 12544.2-a1 |
12544.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.239919898$ |
$3.197869643$ |
1.771847702 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+4$ |
| 87808.2-e1 |
87808.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{20} \cdot 7^{8} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.246817398$ |
$1.208681114$ |
2.755794709 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 1\) , \( 73 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}+73a+5$ |
| 87808.2-o1 |
87808.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{20} \cdot 7^{8} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.208681114$ |
2.791329467 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 2\) , \( -73 a - 5\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a-2\right){x}-73a-5$ |
| 87808.3-e1 |
87808.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{20} \cdot 7^{8} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.246817398$ |
$1.208681114$ |
2.755794709 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a + 1\) , \( -73 a + 78\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+1\right){x}-73a+78$ |
| 87808.3-o1 |
87808.3-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{20} \cdot 7^{8} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.208681114$ |
2.791329467 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 1\) , \( 73 a - 78\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+1\right){x}+73a-78$ |
| 112896.2-o1 |
112896.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 7^{2} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.508038973$ |
$1.846290899$ |
4.332379766 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 0\) , \( -24 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-24a+12$ |
| 112896.2-x1 |
112896.2-x |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 7^{2} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.508038973$ |
$1.846290899$ |
4.332379766 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 1\) , \( 25 a - 13\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}+25a-13$ |
*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.
