| 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-a7 |
450.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$0.82314$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.970717605$ |
0.647145070 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$ |
| 4050.2-c7 |
4050.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4050.2 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 5^{8} \) |
$1.42571$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{7} \) |
$1$ |
$0.323572535$ |
2.588580280 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -2597\) , \( -50281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-2597{x}-50281$ |
| 11250.3-g7 |
11250.3-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
11250.3 |
\( 2 \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{20} \) |
$1.84059$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.448117683$ |
$0.194143521$ |
4.175958957 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -7212\) , \( -232781\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-7212{x}-232781$ |
| 18000.2-f7 |
18000.2-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{14} \cdot 3^{6} \cdot 5^{14} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.217059055$ |
1.736472441 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -4616 i - 3462\) , \( 163878 i + 29796\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-4616i-3462\right){x}+163878i+29796$ |
| 18000.3-g7 |
18000.3-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{14} \cdot 3^{6} \cdot 5^{14} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.217059055$ |
1.736472441 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 4616 i - 3462\) , \( -163878 i + 29796\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(4616i-3462\right){x}-163878i+29796$ |
| 57600.2-ba7 |
57600.2-ba |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 5^{8} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.242679401$ |
2.912152815 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 4616\) , \( -119184 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+4616{x}-119184i$ |
*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.
