| 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 |
| 2916.4-a1 |
2916.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{18} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.878378408$ |
1.132704799 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -29\) , \( -53\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-29{x}-53$ |
| 2916.4-a2 |
2916.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$1.878378408$ |
1.132704799 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$ |
| 2916.4-a3 |
2916.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{6} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$5.635135226$ |
1.132704799 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$ |
| 2916.4-b1 |
2916.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{12} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.289527793$ |
1.983659896 |
\( -\frac{729}{8} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -a\) , \( -2 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-a{x}-2a-1$ |
| 2916.4-b2 |
2916.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{20} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.096509264$ |
1.983659896 |
\( -\frac{4018245}{2} a + \frac{4247199}{2} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 89 a - 90\) , \( -448 a + 61\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(89a-90\right){x}-448a+61$ |
| 2916.4-b3 |
2916.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{8} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$3.289527793$ |
1.983659896 |
\( \frac{4018245}{2} a + 114477 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -12 a + 1\) , \( -14 a + 25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-12a+1\right){x}-14a+25$ |
| 2916.4-c1 |
2916.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{12} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.683432481$ |
$2.333616537$ |
3.846969597 |
\( \frac{3375}{64} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( a + 3\) , \( -6 a - 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a+3\right){x}-6a-3$ |
| 2916.4-c2 |
2916.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{20} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.050297445$ |
$0.777872179$ |
3.846969597 |
\( -\frac{72340125}{4} a + \frac{66954375}{4} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -59 a + 423\) , \( -1838 a - 391\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-59a+423\right){x}-1838a-391$ |
| 2916.4-c3 |
2916.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{8} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.050297445$ |
$2.333616537$ |
3.846969597 |
\( \frac{72340125}{4} a - \frac{2692875}{2} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 5 a + 42\) , \( -57 a + 50\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(5a+42\right){x}-57a+50$ |
| 2916.4-d1 |
2916.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{12} \cdot 3^{12} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.683432481$ |
$2.333616537$ |
3.846969597 |
\( \frac{3375}{64} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a + 4\) , \( 5 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-3a+4\right){x}+5a-9$ |
| 2916.4-d2 |
2916.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{8} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.050297445$ |
$2.333616537$ |
3.846969597 |
\( -\frac{72340125}{4} a + \frac{66954375}{4} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -7 a + 48\) , \( 56 a - 7\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-7a+48\right){x}+56a-7$ |
| 2916.4-d3 |
2916.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{20} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.050297445$ |
$0.777872179$ |
3.846969597 |
\( \frac{72340125}{4} a - \frac{2692875}{2} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 57 a + 364\) , \( 1837 a - 2229\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(57a+364\right){x}+1837a-2229$ |
| 2916.4-e1 |
2916.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{12} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.289527793$ |
1.983659896 |
\( -\frac{729}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -a\) , \( a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}-a{x}+a-2$ |
| 2916.4-e2 |
2916.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{8} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$3.289527793$ |
1.983659896 |
\( -\frac{4018245}{2} a + \frac{4247199}{2} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 10 a - 9\) , \( 13 a + 12\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(10a-9\right){x}+13a+12$ |
| 2916.4-e3 |
2916.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{20} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.096509264$ |
1.983659896 |
\( \frac{4018245}{2} a + 114477 \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -91 a\) , \( 447 a - 386\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}-91a{x}+447a-386$ |
| 2916.4-f1 |
2916.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{6} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$5.635135226$ |
3.398114398 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 2916.4-f2 |
2916.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{22} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.626126136$ |
3.398114398 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-123{x}-667$ |
| 2916.4-f3 |
2916.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2916.4 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{18} \) |
$2.17787$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$1.878378408$ |
3.398114398 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$ |
*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.
