| 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-c1 |
700.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
700.2 |
\( 2^{2} \cdot 5^{2} \cdot 7 \) |
\( 2^{10} \cdot 5^{2} \cdot 7 \) |
$1.21608$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.699948933$ |
2.796898497 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a - 7\) , \( 6 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-7\right){x}+6a-1$ |
| 17500.2-b2 |
17500.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17500.2 |
\( 2^{2} \cdot 5^{4} \cdot 7 \) |
\( 2^{10} \cdot 5^{14} \cdot 7 \) |
$2.71924$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.739989786$ |
1.118759399 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 150 a - 167\) , \( 900 a - 259\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(150a-167\right){x}+900a-259$ |
| 22400.2-j2 |
22400.2-j |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22400.2 |
\( 2^{7} \cdot 5^{2} \cdot 7 \) |
\( 2^{28} \cdot 5^{2} \cdot 7 \) |
$2.89234$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.308129490$ |
1.977705894 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 9 a - 72\) , \( 53 a - 199\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-72\right){x}+53a-199$ |
| 22400.7-j2 |
22400.7-j |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22400.7 |
\( 2^{7} \cdot 5^{2} \cdot 7 \) |
\( 2^{28} \cdot 5^{2} \cdot 7 \) |
$2.89234$ |
$(a), (-a+1), (-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.308129490$ |
1.977705894 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 46 a + 13\) , \( 22 a + 209\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(46a+13\right){x}+22a+209$ |
| 39200.2-a2 |
39200.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39200.2 |
\( 2^{5} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{2} \cdot 7^{7} \) |
$3.32667$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.330659793$ |
$0.699224624$ |
2.796398519 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -98 a - 157\) , \( 947 a + 605\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-98a-157\right){x}+947a+605$ |
| 39200.5-a2 |
39200.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39200.5 |
\( 2^{5} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{2} \cdot 7^{7} \) |
$3.32667$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.322639175$ |
$0.699224624$ |
2.796398519 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 57 a + 205\) , \( 1083 a - 1141\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(57a+205\right){x}+1083a-1141$ |
| 44800.5-n2 |
44800.5-n |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44800.5 |
\( 2^{8} \cdot 5^{2} \cdot 7 \) |
\( 2^{34} \cdot 5^{2} \cdot 7 \) |
$3.43959$ |
$(a), (-a+1), (-2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.227882656$ |
$0.924987233$ |
3.434263157 |
\( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 96 a - 107\) , \( -480 a + 154\bigr] \) |
${y}^2={x}^{3}+\left(96a-107\right){x}-480a+154$ |
*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.
