| 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 |
| 98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
0.309506696 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 784.1-c6 |
784.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{4} \) |
$1.33740$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.218854283$ |
2.785560266 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -10922\) , \( -441166\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-10922{x}-441166$ |
| 4802.1-a6 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{18} \cdot 7^{16} \) |
$2.10397$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$25.26102135$ |
$0.062529795$ |
4.467688722 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-133795{x}+18781197$ |
| 7938.3-d6 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$6.648098301$ |
$0.145902855$ |
5.487015846 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-24575{x}+1488935$ |
| 28322.1-a6 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 17^{6} \) |
$3.27880$ |
$(a), (-2a+3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.106159921$ |
2.702390401 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 32765 a - 2730\) , \( 2095538 a + 2481559\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(32765a-2730\right){x}+2095538a+2481559$ |
| 28322.3-a6 |
28322.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28322.3 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 17^{6} \) |
$3.27880$ |
$(a), (2a+3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.106159921$ |
2.702390401 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -32767 a - 2730\) , \( -2095539 a + 2481559\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-32767a-2730\right){x}-2095539a+2481559$ |
| 38416.1-b6 |
38416.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
38416.1 |
\( 2^{4} \cdot 7^{4} \) |
\( 2^{30} \cdot 7^{16} \) |
$3.53844$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$7.014414334$ |
$0.031264897$ |
1.240576118 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -535181\) , \( 150784758\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-535181{x}+150784758$ |
*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.
