| 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 |
| 1089.1-a1 |
1089.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1089.1 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{2} \) |
$0.88911$ |
$(-2a+1), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.075642846$ |
$5.314975105$ |
0.928471248 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -2\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-2{x}$ |
| 5929.1-a1 |
5929.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5929.1 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{6} \cdot 11^{2} \) |
$1.35814$ |
$(-3a+1), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.479467962$ |
2.008871764 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -5 a + 3\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+3\right){x}-a-1$ |
| 5929.3-a1 |
5929.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5929.3 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{6} \cdot 11^{2} \) |
$1.35814$ |
$(3a-2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.479467962$ |
2.008871764 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 5 a - 2\) , \( a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(5a-2\right){x}+a-2$ |
| 30976.1-c1 |
30976.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30976.1 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.05331$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.605759488$ |
$2.301451730$ |
3.219596600 |
\( \frac{19683}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 9\) , \( a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-9\right){x}+a-5$ |
| 30976.1-f1 |
30976.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30976.1 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.05331$ |
$(2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.605759488$ |
$2.301451730$ |
3.219596600 |
\( \frac{19683}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 9\) , \( -a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+9\right){x}-a-4$ |
| 43681.1-b1 |
43681.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43681.1 |
\( 11^{2} \cdot 19^{2} \) |
\( 11^{2} \cdot 19^{6} \) |
$2.23755$ |
$(-5a+3), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.111956951$ |
1.219338914 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -10 a + 12\) , \( -4 a + 4\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+12\right){x}-4a+4$ |
| 43681.3-b1 |
43681.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43681.3 |
\( 11^{2} \cdot 19^{2} \) |
\( 11^{2} \cdot 19^{6} \) |
$2.23755$ |
$(-5a+2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.111956951$ |
1.219338914 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 9 a + 2\) , \( 3 a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(9a+2\right){x}+3a$ |
| 116281.1-a1 |
116281.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116281.1 |
\( 11^{2} \cdot 31^{2} \) |
\( 11^{2} \cdot 31^{6} \) |
$2.85809$ |
$(-6a+1), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.350460323$ |
$1.653411732$ |
5.156585325 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 13 a - 20\) , \( 13 a - 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a-20\right){x}+13a-9$ |
| 116281.3-a1 |
116281.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
116281.3 |
\( 11^{2} \cdot 31^{2} \) |
\( 11^{2} \cdot 31^{6} \) |
$2.85809$ |
$(6a-5), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.350460323$ |
$1.653411732$ |
5.156585325 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -13 a - 7\) , \( -13 a + 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-13a-7\right){x}-13a+4$ |
| 131769.1-a1 |
131769.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
131769.1 |
\( 3^{2} \cdot 11^{4} \) |
\( 3^{6} \cdot 11^{14} \) |
$2.94885$ |
$(-2a+1), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.483179555$ |
2.231710769 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -204\) , \( 259\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-204{x}+259$ |
*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.
