| 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 |
| 110889.1-CMe1 |
110889.1-CMe |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{10} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$0.400048476$ |
1.385808573 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -1935 a - 269\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-1935a-269$ |
| 110889.1-CMd1 |
110889.1-CMd |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{8} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
$0 \le r \le 2$ |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$4$ |
\( 3^{2} \) |
$1$ |
$0.730263467$ |
3.372942475 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -388 a + 128\bigr] \) |
${y}^2+a{y}={x}^{3}-388a+128$ |
| 110889.1-CMc1 |
110889.1-CMc |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{6} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs[2] |
$1$ |
\( 3 \) |
$1$ |
$1.333050275$ |
4.617821610 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -63 a + 45\bigr] \) |
${y}^2+{y}={x}^{3}-63a+45$ |
| 110889.1-CMc2 |
110889.1-CMc |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{10} \cdot 37^{6} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-27$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$0.444350091$ |
4.617821610 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 990 a - 1200\) , \( -15939 a + 11448\bigr] \) |
${y}^2+{y}={x}^{3}+\left(990a-1200\right){x}-15939a+11448$ |
| 110889.1-CMb1 |
110889.1-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{4} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$2.433399883$ |
2.809848155 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -9 a + 10\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-9a+10$ |
| 110889.1-CMa1 |
110889.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{6} \cdot 37^{2} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.075228606$ |
$4.442019255$ |
4.630352674 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -a + 2\bigr] \) |
${y}^2+a{y}={x}^{3}-a+2$ |
| 110889.1-a1 |
110889.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{9} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3Cn[2], 5S4 |
$1$ |
\( 2 \) |
$1$ |
$0.304427890$ |
0.703046097 |
\( 972 a + 459 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -465 a + 447\) , \( 2796 a + 1346\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-465a+447\right){x}+2796a+1346$ |
| 110889.1-b1 |
110889.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
110889.1 |
\( 3^{4} \cdot 37^{2} \) |
\( 3^{12} \cdot 37^{3} \) |
$2.82437$ |
$(-2a+1), (-7a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3Cn[2], 5S4 |
$1$ |
\( 2 \) |
$1$ |
$1.851762562$ |
4.276462455 |
\( 972 a + 459 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -12 a - 3\) , \( 12 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-12a-3\right){x}+12a-13$ |
*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.
