| 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 |
| 1008.5-a2 |
1008.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1008.5 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{11} \cdot 3^{2} \cdot 7^{8} \) |
$1.33215$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.275008515$ |
$1.402443500$ |
1.351697264 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 13 a - 47\) , \( 50 a - 114\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(13a-47\right){x}+50a-114$ |
| 3528.4-c2 |
3528.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3528.4 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 7^{14} \) |
$1.82209$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.328500770$ |
$0.530073818$ |
3.468844441 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -91 a + 329\) , \( -1246 a - 602\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-91a+329\right){x}-1246a-602$ |
| 4032.7-b2 |
4032.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.7 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{17} \cdot 3^{2} \cdot 7^{8} \) |
$1.88394$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.991677309$ |
1.499275166 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 21 a + 73\) , \( 214 a - 242\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a+73\right){x}+214a-242$ |
| 8064.4-c2 |
8064.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8064.4 |
\( 2^{7} \cdot 3^{2} \cdot 7 \) |
\( 2^{23} \cdot 3^{2} \cdot 7^{8} \) |
$2.24040$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.701221750$ |
2.120295274 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 128 a - 16\) , \( 220 a + 728\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(128a-16\right){x}+220a+728$ |
| 9072.5-b2 |
9072.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9072.5 |
\( 2^{4} \cdot 3^{4} \cdot 7 \) |
\( 2^{11} \cdot 3^{14} \cdot 7^{8} \) |
$2.30735$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.467481166$ |
2.827060365 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 117 a - 423\) , \( -1350 a + 3078\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(117a-423\right){x}-1350a+3078$ |
| 28224.7-f2 |
28224.7-f |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.7 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{17} \cdot 3^{2} \cdot 7^{14} \) |
$3.06438$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.374818791$ |
1.133345496 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -147 a - 512\) , \( -2548 a - 4003\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-147a-512\right){x}-2548a-4003$ |
| 31752.4-a2 |
31752.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
31752.4 |
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{11} \cdot 3^{14} \cdot 7^{14} \) |
$3.15595$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.568362093$ |
$0.176691272$ |
2.974976467 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -816 a + 2960\) , \( 36602 a + 14926\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-816a+2960\right){x}+36602a+14926$ |
| 32256.4-l2 |
32256.4-l |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
32256.4 |
\( 2^{9} \cdot 3^{2} \cdot 7 \) |
\( 2^{29} \cdot 3^{2} \cdot 7^{8} \) |
$3.16840$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.645967249$ |
$0.495838654$ |
4.935515645 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -144 a - 224\) , \( 1388 a + 1016\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-144a-224\right){x}+1388a+1016$ |
| 36288.7-a2 |
36288.7-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.7 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{17} \cdot 3^{14} \cdot 7^{8} \) |
$3.26308$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.330559103$ |
0.999516777 |
\( \frac{70011793}{7203} a - \frac{221078161}{7203} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 189 a + 656\) , \( -5589 a + 7190\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(189a+656\right){x}-5589a+7190$ |
*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.
