| 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 |
| 1792.4-a2 |
1792.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1792.4 |
\( 2^{8} \cdot 7 \) |
\( 2^{23} \cdot 7^{4} \) |
$1.53823$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.906024945$ |
1.440819428 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 11\) , \( 13 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+11\right){x}+13a-5$ |
| 3584.4-d2 |
3584.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.4 |
\( 2^{9} \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.695526328$ |
2.037626376 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 5\) , \( 6 a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-a-5\right){x}+6a-2$ |
| 3584.5-b2 |
3584.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3584.5 |
\( 2^{9} \cdot 7 \) |
\( 2^{23} \cdot 7^{4} \) |
$1.82928$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.245790028$ |
$1.906024945$ |
2.833112381 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 11\) , \( -13 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+11\right){x}-13a+5$ |
| 7168.5-c2 |
7168.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7168.5 |
\( 2^{10} \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$2.17539$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.815201115$ |
$2.695526328$ |
3.322150588 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -a - 5\) , \( -6 a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-a-5\right){x}-6a+2$ |
| 12544.4-a1 |
12544.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.4 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{23} \cdot 7^{10} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.720409714$ |
1.089157111 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 21 a - 79\) , \( 77 a + 209\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(21a-79\right){x}+77a+209$ |
| 14336.7-d1 |
14336.7-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{29} \cdot 7^{4} \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.347763164$ |
2.037626376 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 18\) , \( -25 a + 6\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-5a-18\right){x}-25a+6$ |
| 14336.7-g1 |
14336.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.7 |
\( 2^{11} \cdot 7 \) |
\( 2^{29} \cdot 7^{4} \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.521987998$ |
$1.347763164$ |
4.254466056 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 18\) , \( 25 a - 6\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-5a-18\right){x}+25a-6$ |
| 25088.4-i1 |
25088.4-i |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.4 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{17} \cdot 7^{10} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.917252007$ |
$1.018813188$ |
4.493445480 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 9 a + 30\) , \( -22 a + 122\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a+30\right){x}-22a+122$ |
| 25088.5-a1 |
25088.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.5 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{23} \cdot 7^{10} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.545460209$ |
$0.720409714$ |
4.752734929 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 21 a - 79\) , \( -77 a - 209\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(21a-79\right){x}-77a-209$ |
| 28672.7-b1 |
28672.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.361504906$ |
$1.906024945$ |
3.923365441 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 7 a + 2\) , \( 7 a + 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(7a+2\right){x}+7a+4$ |
| 28672.7-r1 |
28672.7-r |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.7 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7^{4} \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.437376844$ |
$1.906024945$ |
5.041448439 |
\( \frac{24238}{49} a + \frac{20204}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 7 a + 2\) , \( -7 a - 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(7a+2\right){x}-7a-4$ |
*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.
