| 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 |
| 3025.1-a1 |
3025.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{4} \) |
$1.87441$ |
$(5), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.927290336$ |
$3.861052278$ |
2.531666051 |
\( -\frac{127419648}{3025} a - \frac{179201728}{3025} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -10 a - 12\) , \( -25 a - 35\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-10a-12\right){x}-25a-35$ |
| 3025.1-a2 |
3025.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$1.87441$ |
$(5), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.854580672$ |
$7.722104556$ |
2.531666051 |
\( \frac{277929063168}{55} a + \frac{393051407552}{55} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 30 a - 47\) , \( -122 a + 168\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(30a-47\right){x}-122a+168$ |
| 3025.1-b1 |
3025.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$1.87441$ |
$(5), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$16.93058676$ |
1.496466589 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$ |
| 3025.1-b2 |
3025.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{4} \) |
$1.87441$ |
$(5), (11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$16.93058676$ |
1.496466589 |
\( \frac{8120601}{3025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$ |
| 3025.1-b3 |
3025.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{8} \) |
$1.87441$ |
$(5), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.232646692$ |
1.496466589 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$ |
| 3025.1-b4 |
3025.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{8} \cdot 11^{2} \) |
$1.87441$ |
$(5), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$16.93058676$ |
1.496466589 |
\( \frac{22930509321}{6875} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$ |
| 3025.1-c1 |
3025.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{4} \) |
$1.87441$ |
$(5), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.927290336$ |
$3.861052278$ |
2.531666051 |
\( \frac{127419648}{3025} a - \frac{179201728}{3025} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 9 a - 12\) , \( 25 a - 35\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(9a-12\right){x}+25a-35$ |
| 3025.1-c2 |
3025.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$1.87441$ |
$(5), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.854580672$ |
$7.722104556$ |
2.531666051 |
\( -\frac{277929063168}{55} a + \frac{393051407552}{55} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -31 a - 47\) , \( 121 a + 168\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a-47\right){x}+121a+168$ |
*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.
