| 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 |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{2} \) |
$0.97395$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.065967243$ |
$4.775104742$ |
0.952471978 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-a-1\right){x}$ |
| 1152.2-b2 |
1152.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1152.2 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{21} \cdot 3^{2} \) |
$1.37737$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.376508944$ |
2.552400847 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+4{x}$ |
| 1152.5-b2 |
1152.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1152.5 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{2} \) |
$1.37737$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.387552371$ |
1.804819947 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a+7\right){x}$ |
| 2592.2-b2 |
2592.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2592.2 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{15} \cdot 3^{14} \) |
$1.68693$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.591701580$ |
2.406426596 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a - 9\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a-9\right){x}$ |
| 4608.7-a2 |
4608.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4608.7 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{33} \cdot 3^{2} \) |
$1.94790$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.688254472$ |
1.276200423 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3 a - 18\) , \( 3 a - 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(3a-18\right){x}+3a-18$ |
| 7056.2-b2 |
7056.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.2 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{15} \cdot 3^{2} \cdot 7^{6} \) |
$2.16684$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.804819947$ |
2.728631281 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 7 a + 7\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+7\right){x}$ |
| 9216.5-c2 |
9216.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.5 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{33} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.318030242$ |
$1.688254472$ |
3.246962639 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a - 5\) , \( -13 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(14a-5\right){x}-13a+5$ |
| 9216.7-i2 |
9216.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.7 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{33} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.688254472$ |
2.552400847 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3 a - 18\) , \( -3 a + 18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(3a-18\right){x}-3a+18$ |
| 10368.2-b3 |
10368.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10368.2 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{21} \cdot 3^{14} \) |
$2.38568$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.125502981$ |
1.701600565 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( a + 40\) , \( -39 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+40\right){x}-39a+1$ |
| 10368.5-e3 |
10368.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10368.5 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{27} \cdot 3^{14} \) |
$2.38568$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.825423846$ |
$0.795850790$ |
3.972643795 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a + 69\) , \( 20 a + 94\bigr] \) |
${y}^2={x}^{3}+\left(-48a+69\right){x}+20a+94$ |
| 17424.4-b3 |
17424.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17424.4 |
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{15} \cdot 3^{2} \cdot 11^{6} \) |
$2.71628$ |
$(a), (-a+1), (-2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.439748251$ |
2.176694756 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 16 a - 18\) , \( -16 a + 19\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(16a-18\right){x}-16a+19$ |
| 17424.6-b3 |
17424.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17424.6 |
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{15} \cdot 3^{2} \cdot 11^{6} \) |
$2.71628$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.439748251$ |
2.176694756 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -9 a + 25\) , \( 15 a + 19\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a+25\right){x}+15a+19$ |
| 36864.7-a3 |
36864.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{39} \cdot 3^{2} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.193776185$ |
1.804819947 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -21 a + 30\) , \( 9 a + 42\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-21a+30\right){x}+9a+42$ |
| 36864.7-w3 |
36864.7-w |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{39} \cdot 3^{2} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.193776185$ |
1.804819947 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a + 30\) , \( -9 a - 42\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-21a+30\right){x}-9a-42$ |
| 41472.7-b3 |
41472.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41472.7 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{33} \cdot 3^{14} \) |
$3.37385$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.562751490$ |
0.850800282 |
\( \frac{3191}{48} a + \frac{48539}{24} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27 a - 165\) , \( -54 a + 322\bigr] \) |
${y}^2={x}^{3}+\left(27a-165\right){x}-54a+322$ |
*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.
