| 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 |
| 196.1-a6 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.19249$ |
$(2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$3.055247526$ |
$0.437708567$ |
3.670876096 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-86}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{4} \) |
$5.21464$ |
$(2,a), (7)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.437708567$ |
23.36131242 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -10739\) , \( -365009\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-10739{x}-365009$ |
| 98.2-d6 |
98.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-129}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{12} \cdot 7^{4} \) |
$6.38660$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$9.645424961$ |
$0.875417135$ |
26.76357072 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -24228\) , \( -1219856\bigr] \) |
${y}^2+a{x}{y}={x}^3-24228{x}-1219856$ |
| 28.2-d6 |
28.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-903}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \cdot 43^{12} \) |
$6.17692$ |
$(2,a), (2,a+1), (7,a+3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2 \cdot 3^{4} \) |
$1$ |
$0.875417135$ |
28.83783013 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5048733\) , \( 4364278259\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5048733{x}+4364278259$ |
| 14.1-c6 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-301}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{16} \) |
$5.99769$ |
$(2,a+1), (7,a)$ |
$1 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
|
\( 2^{2} \cdot 3^{2} \) |
|
$0.875417135$ |
19.46444913 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -131707\) , \( -15452653\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-131707{x}-15452653$ |
| 28.1-a6 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{301}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$3.56625$ |
$(-23a+211), (2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \cdot 3^{2} \) |
$1$ |
$7.027708105$ |
11.13831196 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 81420567929 a - 747007312908\) , \( -37246591460814439 a + 341725400803283189\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(81420567929a-747007312908\right){x}-37246591460814439a+341725400803283189$ |
*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.
