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-a3 |
218.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
218.3 |
\( 2 \cdot 109 \) |
\( 2^{9} \cdot 109^{3} \) |
$0.90845$ |
$(-a+1), (-4a-7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.538206648$ |
0.639567958 |
\( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -5 a\) , \( a - 5\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-5a{x}+a-5$ |
6976.13-b3 |
6976.13-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6976.13 |
\( 2^{6} \cdot 109 \) |
\( 2^{27} \cdot 109^{3} \) |
$2.16067$ |
$(-a+1), (-4a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.490565254$ |
$0.897391566$ |
2.662255488 |
\( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -9 a - 45\) , \( 74 a - 18\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a-45\right){x}+74a-18$ |
13952.3-h3 |
13952.3-h |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13952.3 |
\( 2^{7} \cdot 109 \) |
\( 2^{15} \cdot 109^{3} \) |
$2.56949$ |
$(a), (-a+1), (-4a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 3^{3} \) |
$0.079771726$ |
$1.794783133$ |
5.844343151 |
\( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 4 a + 10\) , \( -2 a - 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(4a+10\right){x}-2a-11$ |
17658.3-a3 |
17658.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17658.3 |
\( 2 \cdot 3^{4} \cdot 109 \) |
\( 2^{9} \cdot 3^{12} \cdot 109^{3} \) |
$2.72535$ |
$(-a+1), (-4a-7), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.663087980$ |
$0.846068882$ |
5.089077913 |
\( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -40 a + 1\) , \( 12 a + 129\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-40a+1\right){x}+12a+129$ |
23762.4-a3 |
23762.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23762.4 |
\( 2 \cdot 109^{2} \) |
\( 2^{9} \cdot 109^{9} \) |
$2.93534$ |
$(-a+1), (-4a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.243116104$ |
3.308013011 |
\( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -398 a + 638\) , \( 4480 a - 1733\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-398a+638\right){x}+4480a-1733$ |
27904.9-b3 |
27904.9-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27904.9 |
\( 2^{8} \cdot 109 \) |
\( 2^{33} \cdot 109^{3} \) |
$3.05565$ |
$(a), (-a+1), (-4a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.634551662$ |
2.878055814 |
\( \frac{175486627225}{663054848} a + \frac{290993664997}{331527424} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -70 a - 1\) , \( 7 a + 305\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-70a-1\right){x}+7a+305$ |
*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.