| 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 |
| 99.4-a4 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.789273651$ |
0.600092679 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$ |
| 891.6-c4 |
891.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
891.6 |
\( 3^{4} \cdot 11 \) |
\( 3^{17} \cdot 11 \) |
$1.38087$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.263091217$ |
1.600247146 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 7 a - 5\) , \( -11 a - 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-5\right){x}-11a-12$ |
| 1584.4-a4 |
1584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1584.4 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{5} \cdot 11 \) |
$1.59449$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.086305777$ |
$3.394636825$ |
2.485990333 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 2 a - 1\) , \( a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-1\right){x}+a+1$ |
| 3267.6-c4 |
3267.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.6 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{11} \cdot 11^{7} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.181860842$ |
2.507105449 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( a - 39\) , \( -9 a + 86\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-39\right){x}-9a+86$ |
| 3267.9-b4 |
3267.9-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.9 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{11} \cdot 11^{7} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.470877092$ |
$1.181860842$ |
1.574051365 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -20 a + 28\) , \( -5 a - 108\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-20a+28\right){x}-5a-108$ |
| 14256.6-m4 |
14256.6-m |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14256.6 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{12} \cdot 3^{17} \cdot 11 \) |
$2.76174$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.353940709$ |
$1.131545608$ |
4.531140880 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 27 a - 17\) , \( -95 a - 24\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(27a-17\right){x}-95a-24$ |
| 28611.10-c4 |
28611.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.10 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{5} \cdot 11 \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.646640728$ |
1.164350825 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 7 a + 18\) , \( -20 a + 29\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(7a+18\right){x}-20a+29$ |
| 28611.12-c4 |
28611.12-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.12 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{5} \cdot 11 \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.126723656$ |
$1.646640728$ |
7.871409715 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -6 a - 19\) , \( -12 a - 37\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-6a-19\right){x}-12a-37$ |
| 35937.10-d4 |
35937.10-d |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.10 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{11} \cdot 11^{7} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.648963937$ |
$1.181860842$ |
4.338722729 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 23 a + 20\) , \( 14 a - 85\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(23a+20\right){x}+14a-85$ |
| 35937.6-c4 |
35937.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.6 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{11} \cdot 11^{7} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.805802695$ |
$1.181860842$ |
4.040464655 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -28 a + 5\) , \( -51 a + 82\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-28a+5\right){x}-51a+82$ |
*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.
