| 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 |
| 288.2-b1 |
288.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{5} \) |
$1.04119$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.676746415$ |
1.185638761 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 79 a - 32\) , \( -374 a - 215\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(79a-32\right){x}-374a-215$ |
| 288.2-c1 |
288.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{5} \) |
$1.04119$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.676746415$ |
1.185638761 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 81 a - 31\) , \( 294 a + 248\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(81a-31\right){x}+294a+248$ |
| 2592.3-b1 |
2592.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{17} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 720 a - 288\) , \( 8374 a + 4948\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(720a-288\right){x}+8374a+4948$ |
| 2592.3-f1 |
2592.3-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{17} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.558915471$ |
1.580851681 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 720 a - 287\) , \( -9094 a - 4659\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(720a-287\right){x}-9094a-4659$ |
| 6912.2-e1 |
6912.2-e |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{11} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.484034997$ |
1.369057715 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -576 a - 1152\) , \( -12092 a - 12292\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-576a-1152\right){x}-12092a-12292$ |
| 6912.2-j1 |
6912.2-j |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{11} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.788156716$ |
$0.484034997$ |
4.316128133 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -576 a - 1152\) , \( 12092 a + 12292\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-576a-1152\right){x}+12092a+12292$ |
| 6912.3-b1 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{11} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.484034997$ |
1.369057715 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -64 a + 1408\) , \( 13872 a + 2368\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-64a+1408\right){x}+13872a+2368$ |
| 6912.3-m1 |
6912.3-m |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{11} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.152626864$ |
$0.484034997$ |
4.316128133 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -64 a + 1408\) , \( -13872 a - 2368\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-64a+1408\right){x}-13872a-2368$ |
| 9216.2-h1 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.514366890$ |
$0.592819380$ |
2.946351043 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -640 a + 257\) , \( 3060 a - 10437\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-640a+257\right){x}+3060a-10437$ |
| 9216.2-u1 |
9216.2-u |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.543890116$ |
$0.592819380$ |
5.177424439 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -640 a + 257\) , \( -3060 a + 10437\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-640a+257\right){x}-3060a+10437$ |
| 27648.2-c1 |
27648.2-c |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1154 a + 2303\) , \( 25737 a - 46065\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1154a+2303\right){x}+25737a-46065$ |
| 27648.2-bu1 |
27648.2-bu |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.342264428$ |
3.872279978 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1154 a + 2303\) , \( -25737 a + 46065\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1154a+2303\right){x}-25737a+46065$ |
| 27648.3-b1 |
27648.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.521423100$ |
$0.342264428$ |
3.408984042 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 126 a - 2817\) , \( 4863 a - 58305\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(126a-2817\right){x}+4863a-58305$ |
| 27648.3-bt1 |
27648.3-bt |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.342264428$ |
3.872279978 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 126 a - 2817\) , \( -4863 a + 58305\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(126a-2817\right){x}-4863a+58305$ |
*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.
