| 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 |
| 121.1-a2 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$0.51333$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1.851543623$ |
0.427595683 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 14641.1-b2 |
14641.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{22} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1.531150332$ |
$0.168322147$ |
2.380775540 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -1250 a + 1250\) , \( 31239\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-1250a+1250\right){x}+31239$ |
| 20449.1-a2 |
20449.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20449.1 |
\( 11^{2} \cdot 13^{2} \) |
\( 11^{10} \cdot 13^{6} \) |
$1.85083$ |
$(-4a+1), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1.384714261$ |
$0.513525805$ |
3.284367889 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -83 a + 155\) , \( -782 a - 418\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-83a+155\right){x}-782a-418$ |
| 20449.3-a2 |
20449.3-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20449.3 |
\( 11^{2} \cdot 13^{2} \) |
\( 11^{10} \cdot 13^{6} \) |
$1.85083$ |
$(4a-3), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1.384714261$ |
$0.513525805$ |
3.284367889 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 83 a + 72\) , \( 782 a - 1200\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(83a+72\right){x}+782a-1200$ |
| 30976.1-h2 |
30976.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30976.1 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{10} \) |
$2.05331$ |
$(2), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 5 \) |
$1$ |
$0.462885905$ |
2.672473023 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 1427\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-165{x}+1427$ |
| 53361.1-c2 |
53361.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53361.1 |
\( 3^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 7^{6} \cdot 11^{10} \) |
$2.35237$ |
$(-2a+1), (-3a+1), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$2.109281154$ |
$0.404039943$ |
3.936299486 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 156 a + 93\) , \( -1524 a + 2591\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(156a+93\right){x}-1524a+2591$ |
| 53361.3-c2 |
53361.3-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53361.3 |
\( 3^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 7^{6} \cdot 11^{10} \) |
$2.35237$ |
$(-2a+1), (3a-2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$2.109281154$ |
$0.404039943$ |
3.936299486 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 249 a - 93\) , \( 1524 a + 1067\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(249a-93\right){x}+1524a+1067$ |
| 75625.1-b2 |
75625.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75625.1 |
\( 5^{4} \cdot 11^{2} \) |
\( 5^{12} \cdot 11^{10} \) |
$2.56664$ |
$(5), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.1.3 |
$1$ |
\( 5 \) |
$1$ |
$0.370308724$ |
2.137978418 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 258 a\) , \( -2981\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+258a{x}-2981$ |
*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.
