| 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-a3 |
361.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
361.2 |
\( 19^{2} \) |
\( 19^{10} \) |
$0.67465$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$0.225966868$ |
$0.935309008$ |
0.488089257 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -99 a - 31\) , \( -498 a + 74\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-99a-31\right){x}-498a+74$ |
| 61009.2-a2 |
61009.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61009.2 |
\( 13^{2} \cdot 19^{2} \) |
\( 13^{6} \cdot 19^{10} \) |
$2.43247$ |
$(-4a+1), (-5a+3), (-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$9$ |
\( 2 \) |
$1$ |
$0.259408045$ |
5.391694971 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -1705 a + 450\) , \( -24977 a + 20894\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1705a+450\right){x}-24977a+20894$ |
| 61009.8-a2 |
61009.8-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61009.8 |
\( 13^{2} \cdot 19^{2} \) |
\( 13^{6} \cdot 19^{10} \) |
$2.43247$ |
$(4a-3), (-5a+3), (-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.259408045$ |
5.391694971 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -580 a - 1155\) , \( -12873 a - 13415\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-580a-1155\right){x}-12873a-13415$ |
| 61731.2-a2 |
61731.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.2 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{6} \cdot 19^{16} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{3} \) |
$1.182529221$ |
$0.123884704$ |
2.706567867 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 19 a + 6700\) , \( -244436 a + 127622\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a+6700\right){x}-244436a+127622$ |
| 61731.3-a2 |
61731.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.3 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{6} \cdot 19^{16} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{3} \) |
$1.182529221$ |
$0.123884704$ |
2.706567867 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 7731 a - 4308\) , \( -195516 a - 34450\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7731a-4308\right){x}-195516a-34450$ |
| 92416.2-u2 |
92416.2-u |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
92416.2 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{24} \cdot 19^{10} \) |
$2.69858$ |
$(-5a+3), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 1 \) |
$11.02710220$ |
$0.233827252$ |
5.954645201 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2080 a - 1589\) , \( 33952 a - 6339\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2080a-1589\right){x}+33952a-6339$ |
| 130321.3-b2 |
130321.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
130321.3 |
\( 19^{4} \) |
\( 19^{22} \) |
$2.94071$ |
$(-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$9.202414482$ |
$0.049226789$ |
4.184683936 |
\( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -11071 a + 46930\) , \( 3697362 a - 724183\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11071a+46930\right){x}+3697362a-724183$ |
*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.
