| 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-e5 |
525.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.259415011$ |
$14.46234780$ |
1.637397992 |
\( \frac{157551496201}{13125} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 562 a - 1576\) , \( -10688 a + 29830\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(562a-1576\right){x}-10688a+29830$ |
| 525.1-k5 |
525.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
525.1 |
\( 3 \cdot 5^{2} \cdot 7 \) |
\( 3^{2} \cdot 5^{8} \cdot 7^{2} \) |
$1.96014$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.148755400$ |
1.875587480 |
\( \frac{157551496201}{13125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -113\) , \( -469\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-113{x}-469$ |
| 1575.1-l5 |
1575.1-l |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1575.1 |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{8} \cdot 5^{8} \cdot 7^{2} \) |
$2.57969$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.218490740$ |
2.809329036 |
\( \frac{157551496201}{13125} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 337 a - 1013\) , \( 5625 a - 15469\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(337a-1013\right){x}+5625a-15469$ |
| 1575.1-p5 |
1575.1-p |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1575.1 |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{8} \cdot 5^{8} \cdot 7^{2} \) |
$2.57969$ |
$(-a+2), (-a), (-a+1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.218490740$ |
2.809329036 |
\( \frac{157551496201}{13125} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -338 a - 675\) , \( -5625 a - 9844\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-338a-675\right){x}-5625a-9844$ |
*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.
