| 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 |
| 135.6-a2 |
135.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
135.6 |
\( 3^{3} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$1.01023$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.966132324$ |
1.199237719 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 405.6-a2 |
405.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
405.6 |
\( 3^{4} \cdot 5 \) |
\( 3^{18} \cdot 5^{2} \) |
$1.32953$ |
$(-a), (a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.398018874$ |
$1.988710774$ |
1.909276988 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 7 a\) , \( -2 a - 10\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+7a{x}-2a-10$ |
| 675.9-b2 |
675.9-b |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.9 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{8} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.667602323$ |
$2.668135488$ |
2.148272491 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -a + 6\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+6\right){x}-a$ |
| 2025.9-a2 |
2025.9-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2025.9 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{18} \cdot 5^{8} \) |
$1.98811$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.889378496$ |
2.145261649 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -15 a + 63\) , \( 46 a + 109\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-15a+63\right){x}+46a+109$ |
| 3375.10-c2 |
3375.10-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3375.10 |
\( 3^{3} \cdot 5^{3} \) |
\( 3^{6} \cdot 5^{8} \) |
$2.25893$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.244556183$ |
$2.668135488$ |
4.721733021 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( a - 7\) , \( 3 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(a-7\right){x}+3a-4$ |
| 10125.10-e3 |
10125.10-e |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
10125.10 |
\( 3^{4} \cdot 5^{3} \) |
\( 3^{18} \cdot 5^{8} \) |
$2.97292$ |
$(-a), (a-1), (-a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.889378496$ |
2.145261649 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 6 a - 62\) , \( -90 a + 172\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(6a-62\right){x}-90a+172$ |
| 16335.6-b3 |
16335.6-b |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16335.6 |
\( 3^{3} \cdot 5 \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{6} \) |
$3.35054$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.496734088$ |
$1.038570330$ |
3.749507319 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 27 a - 28\) , \( 44 a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(27a-28\right){x}+44a+8$ |
| 16875.13-i3 |
16875.13-i |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.13 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{14} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.336172993$ |
$1.193226464$ |
3.845733729 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 19 a + 2\) , \( -17 a + 64\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(19a+2\right){x}-17a+64$ |
| 34560.6-j3 |
34560.6-j |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.6 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{24} \cdot 3^{6} \cdot 5^{2} \) |
$4.04090$ |
$(-a), (a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.387306403$ |
$1.491533081$ |
2.786834691 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a\) , \( 4 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+12a{x}+4a-48$ |
| 34560.6-p3 |
34560.6-p |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.6 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{24} \cdot 3^{12} \cdot 5^{2} \) |
$4.04090$ |
$(-a), (a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.861137025$ |
2.077140660 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -38 a + 35\) , \( -71 a + 181\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+35\right){x}-71a+181$ |
| 34560.6-bm3 |
34560.6-bm |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
34560.6 |
\( 2^{8} \cdot 3^{3} \cdot 5 \) |
\( 2^{24} \cdot 3^{12} \cdot 5^{2} \) |
$4.04090$ |
$(-a), (a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.423833414$ |
$0.861137025$ |
5.282169709 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -38 a + 35\) , \( 71 a - 181\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38a+35\right){x}+71a-181$ |
| 49005.6-b3 |
49005.6-b |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
49005.6 |
\( 3^{4} \cdot 5 \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{6} \) |
$4.40956$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.419510886$ |
$1.038570330$ |
4.203710339 |
\( -\frac{622427}{675} a + \frac{1187018}{675} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 16 a + 27\) , \( -58 a + 70\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(16a+27\right){x}-58a+70$ |
*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.
