| 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 |
| 3584.2-a2 |
3584.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.2 |
\( 2^{9} \cdot 7 \) |
\( 2^{19} \cdot 7^{10} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.933317072$ |
$0.788612779$ |
2.225532739 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 73 a - 122\) , \( -413 a + 317\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(73a-122\right){x}-413a+317$ |
| 3584.2-f2 |
3584.2-f |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.2 |
\( 2^{9} \cdot 7 \) |
\( 2^{25} \cdot 7^{10} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$0.096522737$ |
$0.557633444$ |
4.068735118 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -195 a + 99\) , \( -823 a + 1750\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-195a+99\right){x}-823a+1750$ |
| 25088.2-a2 |
25088.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.2 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{25} \cdot 7^{16} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$2.486301123$ |
$0.210765630$ |
3.169016362 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1362 a - 692\) , \( -17372 a - 11480\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(1362a-692\right){x}-17372a-11480$ |
| 25088.2-f2 |
25088.2-f |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.2 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{16} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.298067613$ |
4.506358739 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -508 a + 854\) , \( -2908 a - 8648\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-508a+854\right){x}-2908a-8648$ |
| 28672.5-a2 |
28672.5-a |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{37} \cdot 7^{10} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$4.991637207$ |
$0.278816722$ |
4.208262259 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -92 a + 1068\) , \( 9324 a - 3136\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-92a+1068\right){x}+9324a-3136$ |
| 28672.5-l2 |
28672.5-l |
$4$ |
$10$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.5 |
\( 2^{12} \cdot 7 \) |
\( 2^{31} \cdot 7^{10} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.394306389$ |
2.980676135 |
\( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -221 a - 313\) , \( 2723 a + 1155\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-221a-313\right){x}+2723a+1155$ |
*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.
