| 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 |
| 53641.3-a1 |
53641.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53641.3 |
\( 7 \cdot 79 \cdot 97 \) |
\( 7^{3} \cdot 79 \cdot 97^{6} \) |
$2.35545$ |
$(-3a+1), (10a-3), (-11a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.512188760$ |
0.295712319 |
\( \frac{294856156647215124879}{22571042417561113} a - \frac{602097867794750797648}{22571042417561113} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -260 a - 91\) , \( -2580 a + 453\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-260a-91\right){x}-2580a+453$ |
| 53641.3-a2 |
53641.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53641.3 |
\( 7 \cdot 79 \cdot 97 \) |
\( 7 \cdot 79^{3} \cdot 97^{2} \) |
$2.35545$ |
$(-3a+1), (10a-3), (-11a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.536566282$ |
0.295712319 |
\( -\frac{708529824867087}{32473027657} a - \frac{493262952929281}{32473027657} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 40 a - 4\) , \( 11 a - 100\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-4\right){x}+11a-100$ |
| 53641.3-a3 |
53641.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53641.3 |
\( 7 \cdot 79 \cdot 97 \) |
\( 7^{2} \cdot 79^{6} \cdot 97 \) |
$2.35545$ |
$(-3a+1), (10a-3), (-11a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.768283141$ |
0.295712319 |
\( -\frac{554830266418451109}{1155394676091313} a + \frac{215108926072220816}{1155394676091313} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 51\) , \( -250 a - 20\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+51{x}-250a-20$ |
| 53641.3-a4 |
53641.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53641.3 |
\( 7 \cdot 79 \cdot 97 \) |
\( 7^{6} \cdot 79^{2} \cdot 97^{3} \) |
$2.35545$ |
$(-3a+1), (10a-3), (-11a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.256094380$ |
0.295712319 |
\( -\frac{365713622880685600556163}{670127785514257} a + \frac{389205227403206576595827}{670127785514257} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -4220 a - 1436\) , \( -153390 a + 25287\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-4220a-1436\right){x}-153390a+25287$ |
*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.
