| 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-a2 |
288.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.744559956$ |
1.580851681 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -700 a - 1713\) , \( 16307 a + 39944\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-700a-1713\right){x}+16307a+39944$ |
| 288.1-b1 |
288.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.250591196$ |
$15.87756153$ |
1.624328963 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a - 147\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-60a-147\right){x}$ |
| 288.1-b2 |
288.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.125295598$ |
$7.938780765$ |
1.624328963 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+3{x}$ |
| 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-c2 |
288.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.744559956$ |
1.580851681 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -700 a - 1713\) , \( -16307 a - 39944\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-700a-1713\right){x}-16307a-39944$ |
| 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-d2 |
288.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.913960172$ |
$7.744559956$ |
2.889670952 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -33\) , \( 21 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-33{x}+21a$ |
| 288.1-e1 |
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 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$15.87756153$ |
3.240993675 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-3{x}$ |
| 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 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a + 147\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-60a+147\right){x}$ |
| 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 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -100 a - 243\) , \( -3583 a - 8776\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-100a-243\right){x}-3583a-8776$ |
| 288.1-f2 |
288.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.80340$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.913960172$ |
$7.744559956$ |
2.889670952 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -33\) , \( -21 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-33{x}-21a$ |
*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.
