| 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 |
| 23808.1-a1 |
23808.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{8} \cdot 3 \cdot 31 \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$5.017906947$ |
1.448544963 |
\( \frac{2998016}{93} a - \frac{425728}{93} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 2\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-2\right){x}+a+1$ |
| 23808.1-a2 |
23808.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{20} \cdot 3 \cdot 31^{4} \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.254476736$ |
1.448544963 |
\( \frac{2499774004}{2770563} a + \frac{1516133908}{2770563} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 18 a + 13\) , \( a - 50\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(18a+13\right){x}+a-50$ |
| 23808.1-a3 |
23808.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{16} \cdot 3^{2} \cdot 31^{2} \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.508953473$ |
1.448544963 |
\( -\frac{4637360}{2883} a + \frac{2720576}{961} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 7\) , \( -3 a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-7\right){x}-3a-6$ |
| 23808.1-a4 |
23808.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{20} \cdot 3^{4} \cdot 31 \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.254476736$ |
1.448544963 |
\( -\frac{1160560100}{279} a + \frac{385205612}{279} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a - 107\) , \( -183 a - 410\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-22a-107\right){x}-183a-410$ |
| 23808.1-b1 |
23808.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{8} \cdot 3 \cdot 31 \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.240179320$ |
$5.017906947$ |
3.592911016 |
\( \frac{2998016}{93} a - \frac{425728}{93} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 2\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4a-2\right){x}-a-1$ |
| 23808.1-b2 |
23808.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{20} \cdot 3 \cdot 31^{4} \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.240179320$ |
$1.254476736$ |
3.592911016 |
\( \frac{2499774004}{2770563} a + \frac{1516133908}{2770563} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -31 a + 18\) , \( -a + 50\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-31a+18\right){x}-a+50$ |
| 23808.1-b3 |
23808.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{16} \cdot 3^{2} \cdot 31^{2} \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.620089660$ |
$2.508953473$ |
3.592911016 |
\( -\frac{4637360}{2883} a + \frac{2720576}{961} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 9 a - 2\) , \( 3 a + 6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(9a-2\right){x}+3a+6$ |
| 23808.1-b4 |
23808.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23808.1 |
\( 2^{8} \cdot 3 \cdot 31 \) |
\( 2^{20} \cdot 3^{4} \cdot 31 \) |
$1.92256$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.240179320$ |
$1.254476736$ |
3.592911016 |
\( -\frac{1160560100}{279} a + \frac{385205612}{279} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 129 a - 22\) , \( 183 a + 410\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(129a-22\right){x}+183a+410$ |
*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.
