| 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 |
| 2916.1-a1 |
2916.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.13736$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.305934883$ |
$3.305583379$ |
1.556987840 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$ |
| 13122.1-a1 |
13122.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.305934883$ |
$3.305583379$ |
1.348391023 |
\( -\frac{35937}{4} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -6\) , \( -8\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-6{x}-8$ |
| 26244.2-a1 |
26244.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
26244.2 |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{12} \) |
$3.00916$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.305934883$ |
$3.305583379$ |
2.038575609 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$ |
| 13122.5-b1 |
13122.5-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{12} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.305934883$ |
$3.305583379$ |
2.860369308 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$ |
| 26244.5-a1 |
26244.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26244.5 |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{12} \) |
$3.77218$ |
$(-a), (a-1), (2)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.427153329$ |
$3.305583379$ |
6.811700614 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$ |
| 1458.1-n1 |
1458.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.305934883$ |
$19.31991708$ |
2.275005083 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$ |
| 648.1-f1 |
648.1-f |
$2$ |
$3$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( - 2^{6} \cdot 3^{6} \) |
$2.36579$ |
$(-a^2+1), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.033992764$ |
$254.7587691$ |
1.924434430 |
\( -\frac{35937}{4} \) |
\( \bigl[a^{2} + a - 2\) , \( 0\) , \( a^{2} + a - 1\) , \( -a^{2} - 4 a - 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-4a-4\right){x}$ |
| 18.1-c2 |
18.1-c |
$2$ |
$3$ |
3.3.1620.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{6} \) |
$5.82248$ |
$(a+2), (a+1)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.096843165$ |
$254.7587691$ |
2.451887866 |
\( -\frac{35937}{4} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - a - 9\) , \( a^{2} - a - 8\) , \( 44 a^{2} - 59 a - 439\) , \( -324 a^{2} + 453 a + 3267\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-a-8\right){y}={x}^{3}+\left(a^{2}-a-9\right){x}^{2}+\left(44a^{2}-59a-439\right){x}-324a^{2}+453a+3267$ |
*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.
