| 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 |
| 9216.1-d1 |
9216.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.501182392$ |
$3.969390382$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(3a-3\right){x}$ |
| 5184.1-CMc1 |
5184.1-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5184.1 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.51647$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.323130127$ |
2.646260255 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^{3}+27{x}$ |
| 2592.3-e2 |
2592.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.323130127$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^{3}+27{x}$ |
| 288.1-f1 |
288.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$1.80340$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$3.969390382$ |
3.240993675 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12\) , \( 0\bigr] \) |
${y}^2={x}^3+12{x}$ |
| 576.1-j1 |
576.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{18} \) |
$4.01221$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2^{3} \) |
$1$ |
$3.969390382$ |
6.929535958 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^3+27{x}$ |
| 288.1-c1 |
288.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{18} \) |
$4.03253$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$1$ |
$3.969390382$ |
2.898832869 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^3+27{x}$ |
| 2592.1-c2 |
2592.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2592.1 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$2.646260255$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^{3}+27{x}$ |
| 576.1-c1 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.501182392$ |
$7.938780765$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+3{x}$ |
| 288.1-e2 |
288.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$7.938780765$ |
3.240993675 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a + 147\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-60a+147\right){x}$ |
| 64.1-a3 |
64.1-a |
$4$ |
$4$ |
4.4.13824.1 |
$4$ |
$[4, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$17.66965$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.501182392$ |
$378.1454402$ |
3.223797882 |
\( 1728 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + 3\) , \( a^{3} - 4 a\) , \( -a^{2} + 4\) , \( -a^{2} + 4\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+4\right){x}-a^{2}+4$ |
*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.
