| 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 |
| 3025.2-a1 |
3025.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.565328620$ |
$3.457460247$ |
2.045566964 |
\( -\frac{71683416}{11} a - \frac{315047809}{55} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -4 a - 16\) , \( 8 a + 23\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-4a-16\right){x}+8a+23$ |
| 3025.2-a2 |
3025.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{8} \cdot 11^{5} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.391332155$ |
$1.728730123$ |
2.045566964 |
\( \frac{1133816726}{1830125} a - \frac{276639469}{9150625} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 6 a - 13\) , \( -3 a + 24\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-13\right){x}-3a+24$ |
| 3025.2-a3 |
3025.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{4} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.782664310$ |
$3.457460247$ |
2.045566964 |
\( -\frac{1473192}{605} a + \frac{9975041}{3025} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -4 a + 2\) , \( -3 a + 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+2\right){x}-3a+2$ |
| 3025.2-a4 |
3025.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{5} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.565328620$ |
$3.457460247$ |
2.045566964 |
\( \frac{139987946}{14641} a - \frac{113503431}{73205} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 2 a + 4\) , \( 3 a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a+4\right){x}+3a-4$ |
| 3025.2-b1 |
3025.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.565328620$ |
$3.457460247$ |
2.045566964 |
\( \frac{71683416}{11} a - \frac{673464889}{55} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 3 a - 20\) , \( -9 a + 31\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(3a-20\right){x}-9a+31$ |
| 3025.2-b2 |
3025.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{8} \cdot 11^{5} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.391332155$ |
$1.728730123$ |
2.045566964 |
\( -\frac{1133816726}{1830125} a + \frac{5392444161}{9150625} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -6 a - 7\) , \( 3 a + 21\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-6a-7\right){x}+3a+21$ |
| 3025.2-b3 |
3025.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{4} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.782664310$ |
$3.457460247$ |
2.045566964 |
\( \frac{1473192}{605} a + \frac{2609081}{3025} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 4 a - 2\) , \( 3 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(4a-2\right){x}+3a-1$ |
| 3025.2-b4 |
3025.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{5} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.565328620$ |
$3.457460247$ |
2.045566964 |
\( -\frac{139987946}{14641} a + \frac{586436299}{73205} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -3 a + 7\) , \( -4 a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-3a+7\right){x}-4a$ |
| 3025.2-c1 |
3025.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7.082488443$ |
1.338464506 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$ |
| 3025.2-c2 |
3025.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{4} \cdot 11^{4} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.541244221$ |
1.338464506 |
\( \frac{8120601}{3025} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$ |
| 3025.2-c3 |
3025.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{8} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.770622110$ |
1.338464506 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$ |
| 3025.2-c4 |
3025.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{8} \cdot 11^{2} \) |
$1.75335$ |
$(-2a+3), (2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.770622110$ |
1.338464506 |
\( \frac{22930509321}{6875} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$ |
*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.
