| 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 |
| 116964.3-a1 |
116964.3-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{10} \cdot 19^{8} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 1 \) |
$1$ |
$0.319512217$ |
0.368940929 |
\( -\frac{2317155}{2} a - 20353596 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2571 a - 1815\) , \( 44328 a - 4908\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2571a-1815\right){x}+44328a-4908$ |
| 116964.3-a2 |
116964.3-a |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{14} \cdot 3^{10} \cdot 19^{8} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 1 \) |
$1$ |
$0.319512217$ |
0.368940929 |
\( \frac{926085}{128} a - \frac{79521}{16} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -491 a + 693\) , \( 3863 a + 3193\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-491a+693\right){x}+3863a+3193$ |
| 116964.3-b1 |
116964.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 19^{8} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.198483745$ |
2.767779653 |
\( \frac{101967}{722} a + \frac{342492}{361} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 8 a - 31\) , \( 58 a - 9\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-31\right){x}+58a-9$ |
| 116964.3-c1 |
116964.3-c |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 1 \) |
$1$ |
$2.412264341$ |
2.785442933 |
\( -\frac{2317155}{2} a - 20353596 \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -3 a + 41\) , \( 129 a - 50\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-3a+41\right){x}+129a-50$ |
| 116964.3-c2 |
116964.3-c |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{14} \cdot 3^{4} \cdot 19^{2} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 1 \) |
$1$ |
$2.412264341$ |
2.785442933 |
\( \frac{926085}{128} a - \frac{79521}{16} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -6 a - 6\) , \( 16 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-6\right){x}+16a+4$ |
| 116964.3-d1 |
116964.3-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 19^{6} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1.562562219$ |
$0.746391894$ |
5.386834011 |
\( \frac{17268549}{2} a - \frac{246587109}{2} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -538 a + 58\) , \( -5136 a + 3033\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-538a+58\right){x}-5136a+3033$ |
| 116964.3-d2 |
116964.3-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 19^{6} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1.562562219$ |
$0.746391894$ |
5.386834011 |
\( -\frac{17268549}{2} a - 114659280 \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 589 a - 277\) , \( 3514 a + 1359\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(589a-277\right){x}+3514a+1359$ |
| 116964.3-d3 |
116964.3-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 19^{6} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1.562562219$ |
$0.746391894$ |
5.386834011 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 153 a + 48\) , \( -411 a + 1073\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(153a+48\right){x}-411a+1073$ |
| 116964.3-d4 |
116964.3-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 19^{6} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.173618024$ |
$0.746391894$ |
5.386834011 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 72 a + 23\) , \( 159 a - 434\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(72a+23\right){x}+159a-434$ |
| 116964.3-d5 |
116964.3-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.3 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 19^{6} \) |
$2.86228$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.520854073$ |
$0.746391894$ |
5.386834011 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -63 a - 20\) , \( 84 a - 194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-63a-20\right){x}+84a-194$ |
*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.
