| 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 |
| 7203.3-a1 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3 \cdot 7^{32} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.277017646$ |
$0.061576923$ |
1.500845174 |
\( -\frac{1866593950165482334}{99698791708803} a + \frac{793626053533786727}{99698791708803} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -23030 a + 15728\) , \( -663068 a + 1309524\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-23030a+15728\right){x}-663068a+1309524$ |
| 7203.3-a2 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3 \cdot 7^{32} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.277017646$ |
$0.061576923$ |
1.500845174 |
\( \frac{1866593950165482334}{99698791708803} a - \frac{1072967896631695607}{99698791708803} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 23030 a - 7302\) , \( 663068 a + 646456\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(23030a-7302\right){x}+663068a+646456$ |
| 7203.3-a3 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{28} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.638508823$ |
$0.123153847$ |
1.500845174 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1667\) , \( 72764\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1667{x}+72764$ |
| 7203.3-a4 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{4} \cdot 7^{14} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.329813602$ |
$0.985230776$ |
1.500845174 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 48\) , \( 48\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+48{x}+48$ |
| 7203.3-a5 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{8} \cdot 7^{16} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.659627205$ |
$0.492615388$ |
1.500845174 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -197\) , \( 146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-197{x}+146$ |
| 7203.3-a6 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{16} \cdot 7^{14} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.319254411$ |
$0.246307694$ |
1.500845174 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1912\) , \( -32782\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1912{x}-32782$ |
| 7203.3-a7 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{4} \cdot 7^{20} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.319254411$ |
$0.246307694$ |
1.500845174 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2402\) , \( 44246\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2402{x}+44246$ |
| 7203.3-a8 |
7203.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{16} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$0.123153847$ |
1.500845174 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -38417\) , \( 2882228\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-38417{x}+2882228$ |
| 7203.3-b1 |
7203.3-b |
$2$ |
$13$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{26} \cdot 7^{4} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 13$ |
2Cn, 13B.4.2 |
$1$ |
\( 2 \) |
$0.991510447$ |
$0.416956105$ |
1.909488257 |
\( -\frac{1713910976512}{1594323} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -912 a + 912\) , \( 10919\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-912a+912\right){x}+10919$ |
| 7203.3-b2 |
7203.3-b |
$2$ |
$13$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{4} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 13$ |
2Cn, 13B.4.1 |
$1$ |
\( 2 \) |
$0.076270034$ |
$5.420429375$ |
1.909488257 |
\( -\frac{28672}{3} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -2 a + 2\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}-1$ |
| 7203.3-c1 |
7203.3-c |
$2$ |
$13$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{26} \cdot 7^{16} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 13$ |
2Cn, 13B.3.2 |
$1$ |
\( 2 \cdot 13 \) |
$1$ |
$0.059565157$ |
1.788277919 |
\( -\frac{1713910976512}{1594323} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 44704 a\) , \( -3655907\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+44704a{x}-3655907$ |
| 7203.3-c2 |
7203.3-c |
$2$ |
$13$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7203.3 |
\( 3 \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{16} \) |
$1.42586$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 13$ |
2Cn, 13B.3.1 |
$1$ |
\( 2 \) |
$1$ |
$0.774347053$ |
1.788277919 |
\( -\frac{28672}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 114 a\) , \( 473\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+114a{x}+473$ |
*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.
