| 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-a3 |
450.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$0.82314$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.323572535$ |
0.647145070 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 4050.2-c3 |
4050.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4050.2 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{14} \cdot 5^{24} \) |
$1.42571$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{3} \) |
$1$ |
$0.107857511$ |
2.588580280 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4082\) , \( 14681\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4082{x}+14681$ |
| 11250.3-g3 |
11250.3-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
11250.3 |
\( 2 \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{36} \) |
$1.84059$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1.344353050$ |
$0.064714507$ |
4.175958957 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -11337\) , \( 67969\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-11337{x}+67969$ |
| 18000.2-f3 |
18000.2-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{18} \cdot 3^{2} \cdot 5^{30} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.072353018$ |
1.736472441 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -7256 i - 5442\) , \( -47850 i - 8700\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-7256i-5442\right){x}-47850i-8700$ |
| 18000.3-g3 |
18000.3-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{18} \cdot 3^{2} \cdot 5^{30} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.072353018$ |
1.736472441 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 7256 i - 5442\) , \( 47850 i - 8700\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(7256i-5442\right){x}+47850i-8700$ |
| 57600.2-ba3 |
57600.2-ba |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{2} \cdot 5^{24} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.080893133$ |
2.912152815 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 7256\) , \( 34800 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+7256{x}+34800i$ |
*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.
