| 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-a3 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.51333$ |
$(11)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$9.257718117$ |
0.427595683 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 14641.1-b3 |
14641.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{14} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.306230066$ |
$0.841610737$ |
2.380775540 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -40 a + 40\) , \( -221\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-40a+40\right){x}-221$ |
| 20449.1-a3 |
20449.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20449.1 |
\( 11^{2} \cdot 13^{2} \) |
\( 11^{2} \cdot 13^{6} \) |
$1.85083$ |
$(-4a+1), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.276942852$ |
$2.567629028$ |
3.284367889 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -3 a + 5\) , \( 8 a + 2\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+5\right){x}+8a+2$ |
| 20449.3-a3 |
20449.3-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20449.3 |
\( 11^{2} \cdot 13^{2} \) |
\( 11^{2} \cdot 13^{6} \) |
$1.85083$ |
$(4a-3), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.276942852$ |
$2.567629028$ |
3.284367889 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 3 a + 2\) , \( -8 a + 10\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(3a+2\right){x}-8a+10$ |
| 30976.1-h3 |
30976.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30976.1 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.05331$ |
$(2), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$2.314429529$ |
2.672473023 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -13\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-5{x}-13$ |
| 53361.1-c3 |
53361.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53361.1 |
\( 3^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 7^{6} \cdot 11^{2} \) |
$2.35237$ |
$(-2a+1), (-3a+1), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.421856230$ |
$2.020199715$ |
3.936299486 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 6 a + 3\) , \( 6 a - 19\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a+3\right){x}+6a-19$ |
| 53361.3-c3 |
53361.3-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53361.3 |
\( 3^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 7^{6} \cdot 11^{2} \) |
$2.35237$ |
$(-2a+1), (3a-2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.421856230$ |
$2.020199715$ |
3.936299486 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 9 a - 3\) , \( -6 a - 13\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-3\right){x}-6a-13$ |
| 75625.1-b3 |
75625.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75625.1 |
\( 5^{4} \cdot 11^{2} \) |
\( 5^{12} \cdot 11^{2} \) |
$2.56664$ |
$(5), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$1.851543623$ |
2.137978418 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 8 a\) , \( 19\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+8a{x}+19$ |
*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.
