| 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 |
| 361.2-a4 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{6} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.677900606$ |
$2.805927025$ |
0.488089257 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -9 a + 9\) , \( -15\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-9a+9\right){x}-15$ |
| 61009.2-a4 |
61009.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61009.2 |
\( 13^{2} \cdot 19^{2} \) |
\( 13^{6} \cdot 19^{6} \) |
$2.43247$ |
$(-4a+1), (-5a+3), (-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.778224135$ |
5.391694971 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -75 a + 140\) , \( -467 a - 177\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-75a+140\right){x}-467a-177$ |
| 61009.8-a4 |
61009.8-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61009.8 |
\( 13^{2} \cdot 19^{2} \) |
\( 13^{6} \cdot 19^{6} \) |
$2.43247$ |
$(4a-3), (-5a+3), (-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.778224135$ |
5.391694971 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -140 a + 75\) , \( 467 a - 644\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-140a+75\right){x}+467a-644$ |
| 61731.2-a4 |
61731.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.2 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{6} \cdot 19^{12} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2^{3} \) |
$0.394176407$ |
$0.371654113$ |
2.706567867 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 589 a - 140\) , \( -1616 a - 3991\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(589a-140\right){x}-1616a-3991$ |
| 61731.3-a4 |
61731.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.3 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{6} \cdot 19^{12} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2^{3} \) |
$0.394176407$ |
$0.371654113$ |
2.706567867 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 141 a - 588\) , \( 2064 a - 5467\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(141a-588\right){x}+2064a-5467$ |
| 92416.2-u4 |
92416.2-u |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
92416.2 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{24} \cdot 19^{6} \) |
$2.69858$ |
$(-5a+3), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs[2] |
$1$ |
\( 1 \) |
$3.675700734$ |
$0.701481756$ |
5.954645201 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -149\) , \( 797\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-149{x}+797$ |
| 130321.3-b4 |
130321.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
130321.3 |
\( 19^{4} \) |
\( 19^{18} \) |
$2.94071$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2^{2} \) |
$3.067471494$ |
$0.147680369$ |
4.184683936 |
\( -\frac{89915392}{6859} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 3369 a\) , \( 81208\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+3369a{x}+81208$ |
*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.
