| 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 |
| 450.2-a2 |
450.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$0.82314$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.882870421$ |
0.647145070 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 4050.2-c2 |
4050.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4050.2 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 5^{2} \) |
$1.42571$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$1.294290140$ |
2.588580280 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 13\) , \( -61\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+13{x}-61$ |
| 11250.3-g2 |
11250.3-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
11250.3 |
\( 2 \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{14} \) |
$1.84059$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.112029420$ |
$0.776574084$ |
4.175958957 |
\( \frac{357911}{2160} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 38\) , \( -281\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+38{x}-281$ |
| 18000.2-f2 |
18000.2-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{8} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.868236220$ |
1.736472441 |
\( \frac{357911}{2160} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 24 i + 18\) , \( 198 i + 36\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(24i+18\right){x}+198i+36$ |
| 18000.3-g2 |
18000.3-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{8} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.868236220$ |
1.736472441 |
\( \frac{357911}{2160} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -24 i + 18\) , \( -198 i + 36\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-24i+18\right){x}-198i+36$ |
| 57600.2-ba2 |
57600.2-ba |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{32} \cdot 3^{6} \cdot 5^{2} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.970717605$ |
2.912152815 |
\( \frac{357911}{2160} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -24\) , \( -144 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}-24{x}-144i$ |
*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.
