| 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 |
| 110889.3-CMe1 |
110889.3-CMe |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{10} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$0.400048476$ |
1.385808573 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 1934 a - 2203\bigr] \) |
${y}^2+a{y}={x}^{3}+1934a-2203$ |
| 110889.3-CMd1 |
110889.3-CMd |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{8} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
$0 \le r \le 2$ |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$4$ |
\( 3^{2} \) |
$1$ |
$0.730263467$ |
3.372942475 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 387 a - 260\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+387a-260$ |
| 110889.3-CMc1 |
110889.3-CMc |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{6} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs[2] |
$1$ |
\( 3 \) |
$1$ |
$1.333050275$ |
4.617821610 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 63 a - 18\bigr] \) |
${y}^2+{y}={x}^{3}+63a-18$ |
| 110889.3-CMc2 |
110889.3-CMc |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{10} \cdot 37^{6} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-27$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$0.444350091$ |
4.617821610 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -990 a - 210\) , \( 15939 a - 4491\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-990a-210\right){x}+15939a-4491$ |
| 110889.3-CMb1 |
110889.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{4} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$2.433399883$ |
2.809848155 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 8 a + 2\bigr] \) |
${y}^2+a{y}={x}^{3}+8a+2$ |
| 110889.3-CMa1 |
110889.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{2} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.075228606$ |
$4.442019255$ |
4.630352674 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+1$ |
| 110889.3-a1 |
110889.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{9} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3Cn[2], 5S4 |
$1$ |
\( 2 \) |
$1$ |
$0.304427890$ |
0.703046097 |
\( -972 a + 1431 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -447 a + 465\) , \( -2796 a + 4142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-447a+465\right){x}-2796a+4142$ |
| 110889.3-b1 |
110889.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.3 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{3} \) |
$2.82437$ |
$(-2a+1), (-7a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3Cn[2], 5S4 |
$1$ |
\( 2 \) |
$1$ |
$1.851762562$ |
4.276462455 |
\( -972 a + 1431 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 10 a - 13\) , \( -13 a\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-13\right){x}-13a$ |
*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.
