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 |
24025.5-a1 |
24025.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24025.5 |
\( 5^{2} \cdot 31^{2} \) |
\( 5^{2} \cdot 31^{2} \) |
$3.68978$ |
$(-a-1), (a-2), (-3a+4), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.184143922$ |
$5.780453452$ |
1.283757362 |
\( -\frac{262144}{155} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1\) , \( 1\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-{x}+1$ |
24025.5-b1 |
24025.5-b |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24025.5 |
\( 5^{2} \cdot 31^{2} \) |
\( 5^{2} \cdot 31^{10} \) |
$3.68978$ |
$(-a-1), (a-2), (-3a+4), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 5^{2} \) |
$0.302977456$ |
$0.407761090$ |
3.724944061 |
\( -\frac{65626385453056}{143145755} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -840\) , \( -9114\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-840{x}-9114$ |
24025.5-b2 |
24025.5-b |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24025.5 |
\( 5^{2} \cdot 31^{2} \) |
\( 5^{10} \cdot 31^{2} \) |
$3.68978$ |
$(-a-1), (a-2), (-3a+4), (3a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1.514887282$ |
$2.038805454$ |
3.724944061 |
\( \frac{99897344}{96875} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 10\) , \( 6\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+10{x}+6$ |
24025.5-c1 |
24025.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24025.5 |
\( 5^{2} \cdot 31^{2} \) |
\( 5^{4} \cdot 31^{2} \) |
$3.68978$ |
$(-a-1), (a-2), (-3a+4), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.282036137$ |
$4.592178700$ |
7.100398043 |
\( -\frac{117649}{775} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-{x}-2$ |
24025.5-c2 |
24025.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24025.5 |
\( 5^{2} \cdot 31^{2} \) |
\( 5^{2} \cdot 31^{4} \) |
$3.68978$ |
$(-a-1), (a-2), (-3a+4), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.564072274$ |
$2.296089350$ |
7.100398043 |
\( \frac{1948441249}{4805} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -26\) , \( -62\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-26{x}-62$ |
*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.