| 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 |
| 51.1-a1 |
51.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{2} \cdot 17^{2} \) |
$0.67542$ |
$(-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.032029606$ |
$7.122411322$ |
0.322621752 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
| 816.1-a1 |
816.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
816.1 |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{12} \cdot 3^{2} \cdot 17^{2} \) |
$1.35085$ |
$(a), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.561205661$ |
2.518152672 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 1\) , \( a + 4\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a-1\right){x}+a+4$ |
| 867.1-a1 |
867.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
867.1 |
\( 3 \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{8} \) |
$1.37148$ |
$(-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.727438481$ |
2.442966929 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( a + 13\) , \( -18 a - 9\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+13\right){x}-18a-9$ |
| 1377.5-b1 |
1377.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1377.5 |
\( 3^{4} \cdot 17 \) |
\( 3^{14} \cdot 17^{2} \) |
$1.53963$ |
$(-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.374137107$ |
3.357536896 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 4 a\) , \( -5 a - 9\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+4a{x}-5a-9$ |
| 13872.1-b1 |
13872.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13872.1 |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 17^{8} \) |
$2.74295$ |
$(a), (-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.069158875$ |
$0.863719240$ |
5.054886703 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a + 48\) , \( -140 a - 74\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(6a+48\right){x}-140a-74$ |
| 14739.3-a1 |
14739.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14739.3 |
\( 3 \cdot 17^{3} \) |
\( 3^{2} \cdot 17^{8} \) |
$2.78484$ |
$(-a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.727438481$ |
4.885933858 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -a - 12\) , \( 8 a - 25\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-a-12\right){x}+8a-25$ |
| 18513.1-a1 |
18513.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
18513.1 |
\( 3^{2} \cdot 11^{2} \cdot 17 \) |
\( 3^{8} \cdot 11^{6} \cdot 17^{2} \) |
$2.94817$ |
$(-a-1), (a+3), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.239852667$ |
1.753416458 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -17 a - 5\) , \( -48 a + 4\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-17a-5\right){x}-48a+4$ |
| 18513.5-d1 |
18513.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
18513.5 |
\( 3^{2} \cdot 11^{2} \cdot 17 \) |
\( 3^{8} \cdot 11^{6} \cdot 17^{2} \) |
$2.94817$ |
$(-a-1), (a-3), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.365921958$ |
$1.239852667$ |
11.80372591 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 6 a - 21\) , \( -54 a + 25\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(6a-21\right){x}-54a+25$ |
| 22032.5-f1 |
22032.5-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22032.5 |
\( 2^{4} \cdot 3^{4} \cdot 17 \) |
\( 2^{12} \cdot 3^{14} \cdot 17^{2} \) |
$3.07926$ |
$(a), (-a-1), (a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.187068553$ |
1.678768448 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a - 3\) , \( -22 a - 72\bigr] \) |
${y}^2={x}^{3}+\left(18a-3\right){x}-22a-72$ |
| 23409.7-a1 |
23409.7-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.7 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{14} \cdot 17^{8} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.665671940$ |
$0.575812827$ |
2.168286047 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 13 a + 108\) , \( 459 a + 142\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(13a+108\right){x}+459a+142$ |
| 31875.1-a1 |
31875.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
31875.1 |
\( 3 \cdot 5^{4} \cdot 17 \) |
\( 3^{2} \cdot 5^{12} \cdot 17^{2} \) |
$3.37712$ |
$(-a-1), (-2a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.953513121$ |
$1.424482264$ |
15.74158172 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 13 a - 2\) , \( 7 a + 51\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a-2\right){x}+7a+51$ |
| 39168.1-c1 |
39168.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
39168.1 |
\( 2^{8} \cdot 3^{2} \cdot 17 \) |
\( 2^{12} \cdot 3^{8} \cdot 17^{2} \) |
$3.55563$ |
$(a), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.056063047$ |
1.453856123 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a - 8\) , \( 2 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-8\right){x}+2a-14$ |
| 39168.1-k1 |
39168.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
39168.1 |
\( 2^{8} \cdot 3^{2} \cdot 17 \) |
\( 2^{12} \cdot 3^{8} \cdot 17^{2} \) |
$3.55563$ |
$(a), (-a-1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.056063047$ |
1.453856123 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a - 8\) , \( -2 a + 14\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-8\right){x}-2a+14$ |
*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.
