| 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 |
| 288.1-a1 |
288.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.872279978$ |
1.580851681 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3\) , \( 9 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-3{x}+9a$ |
| 288.1-c1 |
288.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.872279978$ |
1.580851681 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -3\) , \( -9 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-3{x}-9a$ |
| 288.1-d1 |
288.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.456980086$ |
$3.872279978$ |
2.889670952 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -100 a - 243\) , \( 3583 a + 8776\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-100a-243\right){x}+3583a+8776$ |
| 288.1-f1 |
288.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.456980086$ |
$3.872279978$ |
2.889670952 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -100 a - 243\) , \( -3583 a - 8776\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-100a-243\right){x}-3583a-8776$ |
| 768.1-h1 |
768.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.706985663$ |
1.369057715 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 6\) , \( -24 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-6\right){x}-24a-60$ |
| 768.1-i1 |
768.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.394078358$ |
$6.706985663$ |
4.316128133 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 6\) , \( -24 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-6\right){x}-24a+60$ |
| 768.1-k1 |
768.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.706985663$ |
1.369057715 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 6\) , \( 24 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-6\right){x}+24a-60$ |
| 768.1-n1 |
768.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.394078358$ |
$6.706985663$ |
4.316128133 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 6\) , \( 24 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-6\right){x}+24a+60$ |
*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.
