| 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 |
| 525.1-c5 |
525.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{9} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1.307450873$ |
$3.059488194$ |
3.491600165 |
\( \frac{46195315900021}{8203125} a + \frac{17098029643466}{1640625} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 225 a - 631\) , \( 2804 a - 7829\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(225a-631\right){x}+2804a-7829$ |
| 525.1-f5 |
525.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3 \cdot 5^{9} \cdot 7 \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.83212381$ |
1.836535274 |
\( \frac{46195315900021}{8203125} a + \frac{17098029643466}{1640625} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -7 a - 55\) , \( 22 a + 112\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-55\right){x}+22a+112$ |
| 1575.1-e5 |
1575.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1575.1 |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{7} \cdot 5^{9} \cdot 7 \) |
$2.57969$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.591241394$ |
$3.575167899$ |
3.690129561 |
\( \frac{46195315900021}{8203125} a + \frac{17098029643466}{1640625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 132 a - 411\) , \( -1416 a + 3831\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(132a-411\right){x}-1416a+3831$ |
| 1575.1-k5 |
1575.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1575.1 |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{7} \cdot 5^{9} \cdot 7 \) |
$2.57969$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.889250867$ |
$4.801423369$ |
3.726873427 |
\( \frac{46195315900021}{8203125} a + \frac{17098029643466}{1640625} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -209 a - 400\) , \( 2720 a + 4787\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-209a-400\right){x}+2720a+4787$ |
*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.
