| 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 |
| 30000.1-a2 |
30000.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30000.1 |
\( 2^{4} \cdot 3 \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$2.03695$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.121183932$ |
$2.388115705$ |
2.005030697 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a + 13\) , \( 22\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-13a+13\right){x}+22$ |
| 22500.3-d2 |
22500.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
22500.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.121183932$ |
$2.388115705$ |
3.472815038 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+22$ |
| 22500.2-a2 |
22500.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$3.09549$ |
$(a), (-a-1), (a-1), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.119882568$ |
$2.388115705$ |
4.858560858 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+22$ |
| 900.2-a2 |
900.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
900.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$2.18884$ |
$(2,a+1), (3,a+1), (3,a+2), (-a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.058435842$ |
$2.388115705$ |
2.995648887 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^3-{x}^2-13{x}+22$ |
| 900.1-a2 |
900.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$3.09549$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \cdot 3 \) |
$0.121183932$ |
$2.388115705$ |
2.196401082 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^3-{x}^2-13{x}+22$ |
| 300.1-b2 |
300.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$4.07389$ |
$(2,a), (3,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.689619051$ |
$2.388115705$ |
7.216310809 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^3-{x}^2-13{x}+22$ |
| 3600.1-d3 |
3600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3600.1 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{6} \) |
$1.54774$ |
$(-2a+1), (2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.121183932$ |
$14.49292130$ |
2.356336058 |
\( \frac{131072}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+22$ |
*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.
