| 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-e4 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.259415011$ |
$14.46234780$ |
1.637397992 |
\( \frac{1771561}{105} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 12 a - 36\) , \( 42 a - 120\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-36\right){x}+42a-120$ |
| 525.1-k4 |
525.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$34.38008640$ |
1.875587480 |
\( \frac{1771561}{105} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-3{x}+1$ |
| 1575.1-l4 |
1575.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1575.1 |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{2} \) |
$2.57969$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.87396296$ |
2.809329036 |
\( \frac{1771561}{105} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 7 a - 23\) , \( -15 a + 41\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-23\right){x}-15a+41$ |
| 1575.1-p4 |
1575.1-p |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1575.1 |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{2} \) |
$2.57969$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.87396296$ |
2.809329036 |
\( \frac{1771561}{105} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -8 a - 15\) , \( 15 a + 26\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-8a-15\right){x}+15a+26$ |
*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.
