| 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 |
| 54756.1-a1 |
54756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.1 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{10} \cdot 13^{6} \) |
$2.36759$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1.476558180$ |
$0.520968436$ |
3.552968318 |
\( \frac{17268549}{2} a - \frac{246587109}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1161 a + 879\) , \( 5112 a - 14564\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-1161a+879\right){x}+5112a-14564$ |
| 54756.1-a2 |
54756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.1 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{10} \cdot 13^{6} \) |
$2.36759$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1.476558180$ |
$0.520968436$ |
3.552968318 |
\( -\frac{17268549}{2} a - 114659280 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1131 a + 189\) , \( -14898 a + 10660\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-1131a+189\right){x}-14898a+10660$ |
| 54756.1-a3 |
54756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.1 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 13^{6} \) |
$2.36759$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.164062020$ |
$1.562905308$ |
3.552968318 |
\( -\frac{132651}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 47 a - 22\) , \( 86 a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(47a-22\right){x}+86a+26$ |
| 54756.1-a4 |
54756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.1 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{18} \cdot 3^{10} \cdot 13^{6} \) |
$2.36759$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1.476558180$ |
$0.520968436$ |
3.552968318 |
\( -\frac{1167051}{512} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 204 a - 96\) , \( 957 a + 388\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(204a-96\right){x}+957a+388$ |
| 54756.1-a5 |
54756.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.1 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 13^{6} \) |
$2.36759$ |
$(-2a+1), (-4a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \) |
$0.492186060$ |
$1.562905308$ |
3.552968318 |
\( \frac{9261}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -21 a + 9\) , \( -18 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-21a+9\right){x}-18a-2$ |
| 54756.1-b1 |
54756.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.1 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 13^{8} \) |
$2.36759$ |
$(-2a+1), (-4a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.397571629$ |
3.227553425 |
\( -\frac{1338000}{169} a - \frac{630375}{338} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -19 a + 41\) , \( 79 a + 7\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-19a+41\right){x}+79a+7$ |
*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.
