| 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 |
| 218.3-a1 |
218.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
218.3 |
\( 2 \cdot 109 \) |
\( 2^{27} \cdot 109 \) |
$0.90845$ |
$(-a+1), (-4a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.846068882$ |
0.639567958 |
\( \frac{93241301714587169}{14629732352} a - \frac{308120979421566003}{7314866176} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -180 a - 170\) , \( -1720 a - 210\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-180a-170\right){x}-1720a-210$ |
| 6976.13-b1 |
6976.13-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6976.13 |
\( 2^{6} \cdot 109 \) |
\( 2^{45} \cdot 109 \) |
$2.16067$ |
$(-a+1), (-4a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.471695762$ |
$0.299130522$ |
2.662255488 |
\( \frac{93241301714587169}{14629732352} a - \frac{308120979421566003}{7314866176} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 491 a - 2985\) , \( 13885 a - 60787\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(491a-2985\right){x}+13885a-60787$ |
| 13952.3-h1 |
13952.3-h |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13952.3 |
\( 2^{7} \cdot 109 \) |
\( 2^{33} \cdot 109 \) |
$2.56949$ |
$(a), (-a+1), (-4a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3^{3} \) |
$0.239315180$ |
$0.598261044$ |
5.844343151 |
\( \frac{93241301714587169}{14629732352} a - \frac{308120979421566003}{7314866176} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 9 a + 700\) , \( -5370 a + 3021\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(9a+700\right){x}-5370a+3021$ |
| 17658.3-a1 |
17658.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17658.3 |
\( 2 \cdot 3^{4} \cdot 109 \) |
\( 2^{27} \cdot 3^{12} \cdot 109 \) |
$2.72535$ |
$(-a+1), (-4a-7), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$1.989263941$ |
$0.282022960$ |
5.089077913 |
\( \frac{93241301714587169}{14629732352} a - \frac{308120979421566003}{7314866176} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -1615 a - 1529\) , \( 48054 a + 7194\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1615a-1529\right){x}+48054a+7194$ |
| 23762.4-a1 |
23762.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23762.4 |
\( 2 \cdot 109^{2} \) |
\( 2^{27} \cdot 109^{7} \) |
$2.93534$ |
$(-a+1), (-4a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$0.081038701$ |
3.308013011 |
\( \frac{93241301714587169}{14629732352} a - \frac{308120979421566003}{7314866176} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -28213 a + 22948\) , \( 929973 a - 3100158\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-28213a+22948\right){x}+929973a-3100158$ |
| 27904.9-b1 |
27904.9-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27904.9 |
\( 2^{8} \cdot 109 \) |
\( 2^{51} \cdot 109 \) |
$3.05565$ |
$(a), (-a+1), (-4a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$0.211517220$ |
2.878055814 |
\( \frac{93241301714587169}{14629732352} a - \frac{308120979421566003}{7314866176} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2870 a - 2721\) , \( 112951 a + 16145\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2870a-2721\right){x}+112951a+16145$ |
*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.
