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 |
132.1-a4 |
132.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.1 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$1.04923$ |
$(a+1), (a), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$13.97852105$ |
1.008812861 |
\( \frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 3 a\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+3a{x}$ |
132.1-b4 |
132.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.1 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$1.04923$ |
$(a+1), (a), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$19.43050189$ |
1.402275687 |
\( \frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2 a - 1\) , \( -a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2a-1\right){x}-a+2$ |
1584.2-e4 |
1584.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1584.2 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{2} \) |
$1.95285$ |
$(a+1), (a), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$10.56800512$ |
1.525360151 |
\( \frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 63 a - 113\) , \( 63 a - 111\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(63a-113\right){x}+63a-111$ |
1584.2-l4 |
1584.2-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1584.2 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{2} \) |
$1.95285$ |
$(a+1), (a), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1.231865029$ |
$8.567043531$ |
3.046516097 |
\( \frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 63 a - 113\) , \( -64 a + 109\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(63a-113\right){x}-64a+109$ |
4356.3-e4 |
4356.3-e |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4356.3 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{8} \) |
$2.51479$ |
$(a+1), (a), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$2.048163752$ |
$3.382416224$ |
3.999733886 |
\( \frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 387 a - 678\) , \( -1338 a + 2322\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(387a-678\right){x}-1338a+2322$ |
4356.3-j4 |
4356.3-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4356.3 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{8} \) |
$2.51479$ |
$(a+1), (a), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.945702835$ |
$2.433348179$ |
3.985837360 |
\( \frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 387 a - 678\) , \( 1338 a - 2322\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(387a-678\right){x}+1338a-2322$ |
*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.