| 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-a2 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{25} \cdot 11^{2} \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.848659206$ |
0.600092679 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5 a + 95\) , \( -252 a - 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5a+95\right){x}-252a-30$ |
| 891.6-c2 |
891.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
891.6 |
\( 3^{4} \cdot 11 \) |
\( 3^{37} \cdot 11^{2} \) |
$1.38087$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.282886402$ |
1.600247146 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -38 a + 850\) , \( 7603 a + 1743\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-38a+850\right){x}+7603a+1743$ |
| 1584.4-a2 |
1584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1584.4 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{25} \cdot 11^{2} \) |
$1.59449$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.690446219$ |
$0.424329603$ |
2.485990333 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -18 a + 379\) , \( -1995 a - 619\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-18a+379\right){x}-1995a-619$ |
| 3267.6-c2 |
3267.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.6 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{31} \cdot 11^{8} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.147732605$ |
2.507105449 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 1816 a + 1776\) , \( 8901 a - 69115\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1816a+1776\right){x}+8901a-69115$ |
| 3267.9-b2 |
3267.9-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.9 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{31} \cdot 11^{8} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.767016737$ |
$0.147732605$ |
1.574051365 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -625 a - 2997\) , \( 18640 a + 68466\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-625a-2997\right){x}+18640a+68466$ |
| 14256.6-m2 |
14256.6-m |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14256.6 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{12} \cdot 3^{37} \cdot 11^{2} \) |
$2.76174$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.831525674$ |
$0.141443201$ |
4.531140880 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -153 a + 3403\) , \( 57577 a + 10236\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-153a+3403\right){x}+57577a+10236$ |
| 28611.10-c2 |
28611.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.10 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{25} \cdot 11^{2} \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.205830091$ |
1.164350825 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1138 a - 7\) , \( 13605 a - 17748\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-1138a-7\right){x}+13605a-17748$ |
| 28611.12-c2 |
28611.12-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.12 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{25} \cdot 11^{2} \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.563361828$ |
$0.205830091$ |
7.871409715 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 1129 a + 196\) , \( 9973 a + 22735\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(1129a+196\right){x}+9973a+22735$ |
| 35937.10-d2 |
35937.10-d |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.10 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{31} \cdot 11^{8} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$5.191711498$ |
$0.147732605$ |
4.338722729 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -1962 a + 1435\) , \( -6716 a + 70431\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-1962a+1435\right){x}-6716a+70431$ |
| 35937.6-c2 |
35937.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.6 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{31} \cdot 11^{8} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.402901347$ |
$0.147732605$ |
4.040464655 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 887 a - 2860\) , \( 31149 a - 56567\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(887a-2860\right){x}+31149a-56567$ |
*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.
