| 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 |
| 396.2-c2 |
396.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
396.2 |
\( 2^{2} \cdot 3^{2} \cdot 11 \) |
\( 2^{2} \cdot 3^{12} \cdot 11^{4} \) |
$1.32208$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.869402865$ |
2.254584685 |
\( \frac{9938375}{176418} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$ |
| 3564.3-c2 |
3564.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3564.3 |
\( 2^{2} \cdot 3^{4} \cdot 11 \) |
\( 2^{2} \cdot 3^{24} \cdot 11^{4} \) |
$2.28991$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{6} \) |
$0.336662039$ |
$0.623134288$ |
4.048176412 |
\( \frac{9938375}{176418} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( -547\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+40{x}-547$ |
| 9900.4-f2 |
9900.4-f |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9900.4 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{6} \cdot 11^{4} \) |
$2.95627$ |
$(-a), (a-1), (-a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.169479672$ |
$0.836022376$ |
4.101194898 |
\( \frac{9938375}{176418} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 13 a - 9\) , \( 81 a - 223\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(13a-9\right){x}+81a-223$ |
| 9900.6-d2 |
9900.6-d |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9900.6 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{6} \cdot 11^{4} \) |
$2.95627$ |
$(-a), (a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.169479672$ |
$0.836022376$ |
4.101194898 |
\( \frac{9938375}{176418} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -14 a + 4\) , \( -81 a - 142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14a+4\right){x}-81a-142$ |
| 13068.2-c2 |
13068.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13068.2 |
\( 2^{2} \cdot 3^{3} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 11^{10} \) |
$3.16874$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.325421268$ |
1.569891268 |
\( \frac{9938375}{176418} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -50 a + 150\) , \( -1733 a + 3194\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-50a+150\right){x}-1733a+3194$ |
| 13068.3-e2 |
13068.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13068.3 |
\( 2^{2} \cdot 3^{3} \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 11^{10} \) |
$3.16874$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.325421268$ |
1.569891268 |
\( \frac{9938375}{176418} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 48 a + 101\) , \( 1732 a + 1461\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(48a+101\right){x}+1732a+1461$ |
| 25344.2-f2 |
25344.2-f |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25344.2 |
\( 2^{8} \cdot 3^{2} \cdot 11 \) |
\( 2^{26} \cdot 3^{12} \cdot 11^{4} \) |
$3.73942$ |
$(-a), (a-1), (-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$0.354617557$ |
$0.467350716$ |
6.396122512 |
\( \frac{9938375}{176418} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( -1296\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+72{x}-1296$ |
*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.
