| 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 |
| 7168.6-a1 |
7168.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.6 |
\( 2^{10} \cdot 7 \) |
\( 2^{21} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.574192918$ |
$2.495279627$ |
2.969327845 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5 a + 22\) , \( -25 a + 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-5a+22\right){x}-25a+2$ |
| 7168.6-b1 |
7168.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.6 |
\( 2^{10} \cdot 7 \) |
\( 2^{21} \cdot 7 \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.495279627$ |
1.886254098 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 22\) , \( 25 a - 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a+22\right){x}+25a-2$ |
| 14336.6-d2 |
14336.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.6 |
\( 2^{11} \cdot 7 \) |
\( 2^{27} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.522939493$ |
$1.764429145$ |
4.062541808 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 27 a - 34\) , \( 73 a - 54\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(27a-34\right){x}+73a-54$ |
| 14336.6-g2 |
14336.6-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.6 |
\( 2^{11} \cdot 7 \) |
\( 2^{27} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.764429145$ |
2.667566128 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 27 a - 34\) , \( -73 a + 54\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(27a-34\right){x}-73a+54$ |
| 14336.7-c2 |
14336.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{15} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.522939493$ |
$3.528858290$ |
4.062541808 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 7 a - 9\) , \( 10 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(7a-9\right){x}+10a$ |
| 14336.7-h2 |
14336.7-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{15} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$3.528858290$ |
2.667566128 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 7 a - 9\) , \( -10 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(7a-9\right){x}-10a$ |
| 28672.7-f2 |
28672.7-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{21} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.324661931$ |
$2.495279627$ |
4.997297996 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14 a + 3\) , \( -15 a + 17\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a+3\right){x}-15a+17$ |
| 28672.7-n2 |
28672.7-n |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{21} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.739190283$ |
$2.495279627$ |
6.561109602 |
\( -\frac{1111000}{7} a - \frac{267000}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a + 3\) , \( 15 a - 17\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a+3\right){x}+15a-17$ |
*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.
