| 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 |
| 12544.2-d3 |
12544.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.459563779$ |
1.287365174 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}+2{x}+2a-1$ |
| 12544.2-h3 |
12544.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12544.2 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$1.63798$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.459563779$ |
1.287365174 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( -2 a + 1\bigr] \) |
${y}^2={x}^{3}+2{x}-2a+1$ |
| 21952.2-f3 |
21952.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
21952.2 |
\( 2^{6} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{10} \) |
$1.88394$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.765156666$ |
$1.685556673$ |
2.978469037 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 10 a + 6\) , \( -20 a + 37\bigr] \) |
${y}^2={x}^{3}+\left(10a+6\right){x}-20a+37$ |
| 21952.3-f3 |
21952.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
21952.3 |
\( 2^{6} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{10} \) |
$1.88394$ |
$(-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.765156666$ |
$1.685556673$ |
2.978469037 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 6\) , \( 20 a + 17\bigr] \) |
${y}^2={x}^{3}+\left(16a-6\right){x}+20a+17$ |
| 28224.2-c3 |
28224.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.2 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$2.00611$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.257561760$ |
$2.574730348$ |
3.062968257 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 9\bigr] \) |
${y}^2={x}^{3}-6{x}+9$ |
| 87808.2-g3 |
87808.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.2 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{10} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.685556673$ |
0.973156599 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 10 a + 6\) , \( 20 a - 37\bigr] \) |
${y}^2={x}^{3}+\left(10a+6\right){x}+20a-37$ |
| 87808.3-h3 |
87808.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87808.3 |
\( 2^{8} \cdot 7^{3} \) |
\( 2^{8} \cdot 7^{10} \) |
$2.66430$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.685556673$ |
0.973156599 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 6\) , \( -20 a - 17\bigr] \) |
${y}^2={x}^{3}+\left(16a-6\right){x}-20a-17$ |
| 112896.2-bi3 |
112896.2-bi |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.574730348$ |
2.973042519 |
\( -\frac{55296}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 6\) , \( -9\bigr] \) |
${y}^2={x}^{3}+\left(-6a+6\right){x}-9$ |
*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.
