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-a2 |
3136.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3136.2 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$1.15823$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.004073929$ |
1.159404707 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59 a + 59\) , \( -138\bigr] \) |
${y}^2={x}^{3}+\left(-59a+59\right){x}-138$ |
12544.2-j2 |
12544.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.284457192$ |
$1.004073929$ |
2.638408062 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( 138\bigr] \) |
${y}^2={x}^{3}-59{x}+138$ |
87808.2-h2 |
87808.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{22} \cdot 7^{14} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.379504273$ |
1.752855156 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 472 a - 295\) , \( 2484 a + 138\bigr] \) |
${y}^2={x}^{3}+\left(472a-295\right){x}+2484a+138$ |
87808.2-j2 |
87808.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{22} \cdot 7^{14} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.554280796$ |
$0.379504273$ |
3.886295808 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -177 a + 472\) , \( -2484 a - 138\bigr] \) |
${y}^2={x}^{3}+\left(-177a+472\right){x}-2484a-138$ |
87808.3-g2 |
87808.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{22} \cdot 7^{14} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.379504273$ |
1.752855156 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 295 a - 472\) , \( -2484 a + 2622\bigr] \) |
${y}^2={x}^{3}+\left(295a-472\right){x}-2484a+2622$ |
87808.3-j2 |
87808.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{22} \cdot 7^{14} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.554280796$ |
$0.379504273$ |
3.886295808 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 295 a - 472\) , \( 2484 a - 2622\bigr] \) |
${y}^2={x}^{3}+\left(295a-472\right){x}+2484a-2622$ |
112896.2-n2 |
112896.2-n |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{6} \cdot 7^{8} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.198526963$ |
$0.579702353$ |
4.252495961 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 177 a - 177\) , \( 828 a - 414\bigr] \) |
${y}^2={x}^{3}+\left(177a-177\right){x}+828a-414$ |
112896.2-v2 |
112896.2-v |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 3^{6} \cdot 7^{8} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.198526963$ |
$0.579702353$ |
4.252495961 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 177 a - 177\) , \( -828 a + 414\bigr] \) |
${y}^2={x}^{3}+\left(177a-177\right){x}-828a+414$ |
*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.