| 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 |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$1.14784$ |
$(5), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.329657945$ |
$7.082488443$ |
1.347996592 |
\( \frac{59319}{55} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}$ |
| 22275.8-a1 |
22275.8-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.8 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.496724502$ |
$2.360829481$ |
5.657230102 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 7\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+7{x}-8$ |
| 605.1-a1 |
605.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
605.1 |
\( 5 \cdot 11^{2} \) |
\( 2^{12} \cdot 5^{2} \cdot 11^{2} \) |
$1.71642$ |
$(5,a+2), (11)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.786066235$ |
$7.082488443$ |
1.437471977 |
\( \frac{59319}{55} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a - 3\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a-3\right){x}$ |
| 605.2-a1 |
605.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{2} \) |
$4.85476$ |
$(5,a), (11,a+5), (11,a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.318631780$ |
$7.082488443$ |
1.705095803 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 7\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2+7{x}-8$ |
| 55.1-b1 |
55.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{2} \) |
$6.25174$ |
$(5,a), (11,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.452752300$ |
$14.16497688$ |
7.614989644 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 7\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2+7{x}-8$ |
| 3025.1-d1 |
3025.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3025.1 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{2} \cdot 11^{2} \) |
$2.29568$ |
$(-2a+1), (2a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.318631780$ |
$11.85112914$ |
2.255602931 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -46 a + 79\) , \( 182 a - 316\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-46a+79\right){x}+182a-316$ |
| 275.1-b1 |
275.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$2.09040$ |
$(-4a-9), (5)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.858870826$ |
$11.85112914$ |
1.917440855 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 299 a + 709\) , \( -3776 a - 8958\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(299a+709\right){x}-3776a-8958$ |
*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.
