| 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-a2 |
288.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{10} \) |
$1.04119$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.168950466$ |
$2.345364298$ |
1.120765359 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 5 a + 22\) , \( -26 a + 23\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(5a+22\right){x}-26a+23$ |
| 288.2-d2 |
288.2-d |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{10} \) |
$1.04119$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.345364298$ |
1.658422999 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 5 a + 22\) , \( 26 a - 23\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(5a+22\right){x}+26a-23$ |
| 2592.3-a2 |
2592.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.240339345$ |
$0.781788099$ |
2.742676397 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 45 a + 199\) , \( -747 a + 424\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(45a+199\right){x}-747a+424$ |
| 2592.3-g2 |
2592.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2592.3 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.80340$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.781788099$ |
2.211230666 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 45 a + 198\) , \( 702 a - 621\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(45a+198\right){x}+702a-621$ |
| 6912.2-f2 |
6912.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.677048354$ |
1.914981930 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 156 a - 168\) , \( 1224 a - 504\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(156a-168\right){x}+1224a-504$ |
| 6912.2-i2 |
6912.2-i |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.265468825$ |
$0.677048354$ |
4.066944035 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 156 a - 168\) , \( -1224 a + 504\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(156a-168\right){x}-1224a+504$ |
| 6912.3-g2 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.677048354$ |
1.914981930 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -196 a - 8\) , \( 856 a - 1336\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-196a-8\right){x}+856a-1336$ |
| 6912.3-h2 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.061875302$ |
$0.677048354$ |
4.066944035 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -196 a - 8\) , \( -856 a + 1336\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-196a-8\right){x}-856a+1336$ |
| 9216.2-k2 |
9216.2-k |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{10} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.829211499$ |
2.345364298 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -40 a - 176\) , \( -368 a - 832\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-40a-176\right){x}-368a-832$ |
| 9216.2-s2 |
9216.2-s |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{10} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.829211499$ |
2.345364298 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a - 176\) , \( 368 a + 832\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-40a-176\right){x}+368a+832$ |
| 27648.2-g2 |
27648.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.744183548$ |
$0.478745482$ |
3.715889911 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -310 a + 335\) , \( 697 a + 5231\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-310a+335\right){x}+697a+5231$ |
| 27648.2-bo2 |
27648.2-bo |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.2 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.478745482$ |
2.708193418 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -310 a + 335\) , \( -697 a - 5231\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-310a+335\right){x}-697a-5231$ |
| 27648.3-t2 |
27648.3-t |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.686045887$ |
$0.478745482$ |
3.715889911 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 390 a + 15\) , \( -2281 a - 3409\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(390a+15\right){x}-2281a-3409$ |
| 27648.3-bd2 |
27648.3-bd |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
27648.3 |
\( 2^{10} \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{16} \) |
$3.25911$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.478745482$ |
2.708193418 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 390 a + 15\) , \( 2281 a + 3409\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(390a+15\right){x}+2281a+3409$ |
*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.
