| 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 |
| 19600.2-a1 |
19600.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.2 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{15} \cdot 5^{4} \cdot 7^{7} \) |
$2.79738$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.864691892$ |
1.307291261 |
\( \frac{213679549}{5600} a - \frac{179378183}{2800} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -17 a - 125\) , \( 114 a + 602\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-17a-125\right){x}+114a+602$ |
| 19600.2-a2 |
19600.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.2 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{21} \cdot 5^{2} \cdot 7^{8} \) |
$2.79738$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.864691892$ |
1.307291261 |
\( \frac{797873}{5120} a + \frac{1579467}{17920} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 9 a - 38\) , \( 61 a + 126\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(9a-38\right){x}+61a+126$ |
| 19600.2-b1 |
19600.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.2 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{2} \cdot 7^{2} \) |
$2.79738$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2.754414524$ |
2.082141668 |
\( \frac{1632207}{10} a - \frac{439487}{5} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 12 a - 3\) , \( 5 a + 16\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(12a-3\right){x}+5a+16$ |
| 19600.2-c1 |
19600.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.2 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{2} \cdot 7^{8} \) |
$2.79738$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.088289041$ |
$0.771282668$ |
6.177071071 |
\( -\frac{11943401}{1024} a - \frac{38773193}{2560} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -23 a - 127\) , \( -166 a - 585\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-23a-127\right){x}-166a-585$ |
| 19600.2-d1 |
19600.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.2 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{2} \cdot 7^{3} \) |
$2.79738$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.287749528$ |
$2.574802917$ |
6.720797884 |
\( \frac{13281}{320} a + \frac{185357}{160} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a - 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-1\right){x}$ |
| 19600.2-d2 |
19600.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19600.2 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{11} \cdot 5^{4} \cdot 7^{3} \) |
$2.79738$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.143874764$ |
$2.574802917$ |
6.720797884 |
\( -\frac{15613}{200} a + \frac{251591}{100} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 3 a - 8\) , \( -5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3a-8\right){x}-5$ |
*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.
