| 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-a4 |
324.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{18} \cdot 3^{10} \) |
$0.65665$ |
$(-2a+1), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$1.878378408$ |
0.722988186 |
\( -\frac{1167051}{512} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -14 a + 13\) , \( 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-14a+13\right){x}+29$ |
| 15876.1-b4 |
15876.1-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
15876.1 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{6} \) |
$1.73734$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 1 \) |
$1$ |
$1.229687320$ |
1.419920610 |
\( -\frac{1167051}{512} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 13 a - 36\) , \( -65 a + 120\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(13a-36\right){x}-65a+120$ |
| 15876.3-b4 |
15876.3-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{6} \) |
$1.73734$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 1 \) |
$1$ |
$1.229687320$ |
1.419920610 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 36 a - 14\) , \( 65 a + 55\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(36a-14\right){x}+65a+55$ |
| 20736.1-d4 |
20736.1-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20736.1 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{42} \cdot 3^{4} \) |
$1.85729$ |
$(-2a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.813361710$ |
1.878378408 |
\( -\frac{1167051}{512} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( 343 a - 208\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+73\right){x}+343a-208$ |
| 20736.1-e4 |
20736.1-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20736.1 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{42} \cdot 3^{4} \) |
$1.85729$ |
$(-2a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.813361710$ |
1.878378408 |
\( -\frac{1167051}{512} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a - 73\) , \( -343 a + 135\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(74a-73\right){x}-343a+135$ |
| 20736.1-f4 |
20736.1-f |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20736.1 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{42} \cdot 3^{10} \) |
$1.85729$ |
$(-2a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$0.693964260$ |
$0.469594602$ |
3.010367773 |
\( -\frac{1167051}{512} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 219 a\) , \( -1654\bigr] \) |
${y}^2={x}^{3}+219a{x}-1654$ |
| 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 |
\( -\frac{1167051}{512} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 204 a - 96\) , \( 957 a + 388\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(204a-96\right){x}+957a+388$ |
| 54756.3-a4 |
54756.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54756.3 |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \) |
\( 2^{18} \cdot 3^{10} \cdot 13^{6} \) |
$2.36759$ |
$(-2a+1), (4a-3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1.476558180$ |
$0.520968436$ |
3.552968318 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 109 a + 96\) , \( -958 a + 1346\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(109a+96\right){x}-958a+1346$ |
| 116964.1-d4 |
116964.1-d |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116964.1 |
\( 2^{2} \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{18} \cdot 3^{4} \cdot 19^{6} \) |
$2.86228$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.173618024$ |
$0.746391894$ |
5.386834011 |
\( -\frac{1167051}{512} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -24 a - 72\) , \( -160 a - 275\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-24a-72\right){x}-160a-275$ |
| 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 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 72 a + 23\) , \( 159 a - 434\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(72a+23\right){x}+159a-434$ |
*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.
