| 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 |
| 92.1-a1 |
92.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( - 2^{4} \cdot 23 \) |
$0.95869$ |
$(a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$20.19010287$ |
1.457095166 |
\( \frac{11904}{23} a + \frac{22288}{23} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+2\right){x}$ |
| 92.1-b1 |
92.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( - 2^{4} \cdot 23 \) |
$0.95869$ |
$(a+1), (-3a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.727437754$ |
$28.37984338$ |
0.993262314 |
\( \frac{11904}{23} a + \frac{22288}{23} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}-a$ |
| 2116.3-a1 |
2116.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2116.3 |
\( 2^{2} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{7} \) |
$2.09946$ |
$(a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.912628166$ |
3.388435388 |
\( \frac{11904}{23} a + \frac{22288}{23} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -7 a - 8\) , \( -6 a - 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-7a-8\right){x}-6a-22$ |
| 2116.3-b1 |
2116.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2116.3 |
\( 2^{2} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{7} \) |
$2.09946$ |
$(a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$6.367253096$ |
0.919033822 |
\( \frac{11904}{23} a + \frac{22288}{23} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -9 a - 11\) , \( -2 a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-9a-11\right){x}-2a+12$ |
| 3312.1-b1 |
3312.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3312.1 |
\( 2^{4} \cdot 3^{2} \cdot 23 \) |
\( - 2^{4} \cdot 3^{6} \cdot 23 \) |
$2.34829$ |
$(a+1), (a), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$17.63012550$ |
2.544689426 |
\( \frac{11904}{23} a + \frac{22288}{23} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2 a - 3\) , \( a + 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-3\right){x}+a+2$ |
| 3312.1-n1 |
3312.1-n |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3312.1 |
\( 2^{4} \cdot 3^{2} \cdot 23 \) |
\( - 2^{4} \cdot 3^{6} \cdot 23 \) |
$2.34829$ |
$(a+1), (a), (-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.190943805$ |
$10.83357683$ |
3.724538900 |
\( \frac{11904}{23} a + \frac{22288}{23} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -2 a - 3\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}-a-2$ |
*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.
