| 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-a3 |
288.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.04119$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.337900933$ |
$4.690728597$ |
1.120765359 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 2\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+2{x}+1$ |
| 288.2-d3 |
288.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.04119$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.690728597$ |
1.658422999 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 2\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+2{x}-1$ |
| 2592.3-a3 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{20} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.620169672$ |
$1.563576199$ |
2.742676397 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 19\) , \( 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+19{x}+10$ |
| 2592.3-g3 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{20} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.563576199$ |
2.211230666 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 18\) , \( -27\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+18{x}-27$ |
| 6912.2-f3 |
6912.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.354096709$ |
1.914981930 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 16 a - 8\) , \( 8 a - 40\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(16a-8\right){x}+8a-40$ |
| 6912.2-i3 |
6912.2-i |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.530937651$ |
$1.354096709$ |
4.066944035 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 8\) , \( -8 a + 40\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a-8\right){x}-8a+40$ |
| 6912.3-g3 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.354096709$ |
1.914981930 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -16 a - 8\) , \( -8 a - 40\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-8\right){x}-8a-40$ |
| 6912.3-h3 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.530937651$ |
$1.354096709$ |
4.066944035 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -16 a - 8\) , \( 8 a + 40\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-8\right){x}+8a+40$ |
| 9216.2-k3 |
9216.2-k |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{8} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.658422999$ |
2.345364298 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -16\) , \( -16 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-16{x}-16a$ |
| 9216.2-s3 |
9216.2-s |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{8} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.658422999$ |
2.345364298 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -16\) , \( 16 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-16{x}+16a$ |
| 27648.2-g3 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.372091774$ |
$0.957490965$ |
3.715889911 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -30 a + 15\) , \( 49 a + 47\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a+15\right){x}+49a+47$ |
| 27648.2-bo3 |
27648.2-bo |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.957490965$ |
2.708193418 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -30 a + 15\) , \( -49 a - 47\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a+15\right){x}-49a-47$ |
| 27648.3-t3 |
27648.3-t |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.372091774$ |
$0.957490965$ |
3.715889911 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 30 a + 15\) , \( -49 a + 47\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a+15\right){x}-49a+47$ |
| 27648.3-bd3 |
27648.3-bd |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{14} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.957490965$ |
2.708193418 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 30 a + 15\) , \( 49 a - 47\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(30a+15\right){x}+49a-47$ |
*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.
