| 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 |
| 324.1-a5 |
324.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{6} \cdot 3^{6} \) |
$0.65665$ |
$(-2a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$5.635135226$ |
0.722988186 |
\( \frac{9261}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( a - 2\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-2\right){x}-1$ |
| 15876.1-b5 |
15876.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
15876.1 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{6} \) |
$1.73734$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 1 \) |
$1$ |
$1.229687320$ |
1.419920610 |
\( \frac{9261}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -13 a + 32\) , \( -33 a + 50\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-13a+32\right){x}-33a+50$ |
| 15876.3-b5 |
15876.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{6} \) |
$1.73734$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 1 \) |
$1$ |
$1.229687320$ |
1.419920610 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -32 a + 12\) , \( 32 a + 18\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-32a+12\right){x}+32a+18$ |
| 20736.1-d5 |
20736.1-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20736.1 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{30} \cdot 3^{12} \) |
$1.85729$ |
$(-2a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$0.813361710$ |
1.878378408 |
\( \frac{9261}{8} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -63\) , \( 156 a - 78\bigr] \) |
${y}^2={x}^{3}-63{x}+156a-78$ |
| 20736.1-e5 |
20736.1-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20736.1 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{30} \cdot 3^{12} \) |
$1.85729$ |
$(-2a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \) |
$1$ |
$0.813361710$ |
1.878378408 |
\( \frac{9261}{8} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -63 a + 63\) , \( -156 a + 78\bigr] \) |
${y}^2={x}^{3}+\left(-63a+63\right){x}-156a+78$ |
| 20736.1-f5 |
20736.1-f |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20736.1 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{30} \cdot 3^{6} \) |
$1.85729$ |
$(-2a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2^{2} \) |
$0.231321420$ |
$1.408783806$ |
3.010367773 |
\( \frac{9261}{8} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21 a\) , \( 26\bigr] \) |
${y}^2={x}^{3}-21a{x}+26$ |
| 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 |
\( \frac{9261}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -21 a + 9\) , \( -18 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-21a+9\right){x}-18a-2$ |
| 54756.3-a5 |
54756.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.3 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 13^{6} \) |
$2.36759$ |
$(-2a+1), (4a-3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \) |
$0.492186060$ |
$1.562905308$ |
3.552968318 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -11 a - 9\) , \( 17 a - 19\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-11a-9\right){x}+17a-19$ |
| 116964.1-d5 |
116964.1-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.1 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 19^{6} \) |
$2.86228$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.520854073$ |
$0.746391894$ |
5.386834011 |
\( \frac{9261}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 19 a + 63\) , \( -84 a - 110\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(19a+63\right){x}-84a-110$ |
| 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.
