| 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 |
| 700.2-b5 |
700.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{55} \cdot 5^{2} \cdot 7^{2} \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.224894973$ |
1.530041583 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1892 a + 1470\) , \( -17927 a + 53305\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1892a+1470\right){x}-17927a+53305$ |
| 17500.2-d4 |
17500.2-d |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17500.2 |
\( 2^{2} \cdot 5^{4} \cdot 7 \) |
\( 2^{55} \cdot 5^{14} \cdot 7^{2} \) |
$2.71924$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.044978994$ |
1.836049899 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -47288 a + 36749\) , \( -2146207 a + 6589586\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-47288a+36749\right){x}-2146207a+6589586$ |
| 22400.2-l4 |
22400.2-l |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22400.2 |
\( 2^{7} \cdot 5^{2} \cdot 7 \) |
\( 2^{73} \cdot 5^{2} \cdot 7^{2} \) |
$2.89234$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.079512380$ |
3.245708337 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -5891 a + 21855\) , \( 714881 a + 267810\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-5891a+21855\right){x}+714881a+267810$ |
| 22400.7-a4 |
22400.7-a |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22400.7 |
\( 2^{7} \cdot 5^{2} \cdot 7 \) |
\( 2^{73} \cdot 5^{2} \cdot 7^{2} \) |
$2.89234$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$9.619282387$ |
$0.079512380$ |
2.312695188 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -11131 a - 8627\) , \( -807247 a + 7749\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-11131a-8627\right){x}-807247a+7749$ |
| 39200.2-p4 |
39200.2-p |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39200.2 |
\( 2^{5} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{67} \cdot 5^{2} \cdot 7^{8} \) |
$3.32667$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1$ |
$0.042501155$ |
3.469808164 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 17629 a + 58863\) , \( -4895362 a + 5973818\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17629a+58863\right){x}-4895362a+5973818$ |
| 39200.5-i4 |
39200.5-i |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39200.5 |
\( 2^{5} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{67} \cdot 5^{2} \cdot 7^{8} \) |
$3.32667$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$17.12146187$ |
$0.042501155$ |
4.400606533 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -4390 a - 69153\) , \( 662316 a + 6962350\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-4390a-69153\right){x}+662316a+6962350$ |
| 44800.5-l4 |
44800.5-l |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44800.5 |
\( 2^{8} \cdot 5^{2} \cdot 7 \) |
\( 2^{79} \cdot 5^{2} \cdot 7^{2} \) |
$3.43959$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{5} \) |
$1$ |
$0.056223743$ |
3.060083166 |
\( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -30264 a + 23520\) , \( 1086752 a - 3364460\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-30264a+23520\right){x}+1086752a-3364460$ |
*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.
