| 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-a5 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{14} \cdot 11^{4} \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.697318412$ |
0.600092679 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -10 a\) , \( -20 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-10a{x}-20a+22$ |
| 891.6-c5 |
891.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
891.6 |
\( 3^{4} \cdot 11 \) |
\( 3^{26} \cdot 11^{4} \) |
$1.38087$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.565772804$ |
1.600247146 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -83 a - 5\) , \( 439 a - 426\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-83a-5\right){x}+439a-426$ |
| 1584.4-a5 |
1584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1584.4 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{14} \cdot 11^{4} \) |
$1.59449$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.345223109$ |
$0.848659206$ |
2.485990333 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -38 a - 1\) , \( -119 a + 177\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a-1\right){x}-119a+177$ |
| 3267.6-c5 |
3267.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.6 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{20} \cdot 11^{10} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.295465210$ |
2.507105449 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -169 a + 361\) , \( -2627 a - 4644\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-169a+361\right){x}-2627a-4644$ |
| 3267.9-b5 |
3267.9-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.9 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{20} \cdot 11^{10} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.883508368$ |
$0.295465210$ |
1.574051365 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 290 a - 132\) , \( 3667 a + 2142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(290a-132\right){x}+3667a+2142$ |
| 14256.6-m5 |
14256.6-m |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14256.6 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{12} \cdot 3^{26} \cdot 11^{4} \) |
$2.76174$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.415762837$ |
$0.282886402$ |
4.531140880 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -333 a - 17\) , \( 3865 a - 4056\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-333a-17\right){x}+3865a-4056$ |
| 28611.10-c5 |
28611.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.10 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{14} \cdot 11^{4} \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.411660182$ |
1.164350825 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -3 a - 222\) , \( 54 a - 2241\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-3a-222\right){x}+54a-2241$ |
| 28611.12-c5 |
28611.12-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.12 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{14} \cdot 11^{4} \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1.126723656$ |
$0.411660182$ |
7.871409715 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -16 a + 221\) , \( 1484 a + 473\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-16a+221\right){x}+1484a+473$ |
| 35937.10-d5 |
35937.10-d |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.10 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{20} \cdot 11^{10} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.595855749$ |
$0.295465210$ |
4.338722729 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -147 a - 380\) , \( 2722 a + 4365\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-147a-380\right){x}+2722a+4365$ |
| 35937.6-c5 |
35937.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.6 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{20} \cdot 11^{10} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \cdot 3 \) |
$0.201450673$ |
$0.295465210$ |
4.040464655 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 282 a + 165\) , \( -553 a - 5868\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(282a+165\right){x}-553a-5868$ |
*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.
