| 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 |
| 150.1-a3 |
150.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
150.1 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$1.08331$ |
$(a+1), (a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.081141989 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 150.1-b3 |
150.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
150.1 |
\( 2 \cdot 3 \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$1.08331$ |
$(a+1), (a), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.341872283$ |
1.549460648 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -455\) , \( 543\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-455{x}+543$ |
| 3600.1-g3 |
3600.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3600.1 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 5^{24} \) |
$2.39775$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$8.562837774$ |
$0.373629380$ |
3.694265501 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -5442\) , \( 13050 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-5442{x}+13050a$ |
| 3600.1-o3 |
3600.1-o |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3600.1 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 5^{24} \) |
$2.39775$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$8.562837774$ |
$0.373629380$ |
3.694265501 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5442\) , \( -13050 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}-5442{x}-13050a$ |
| 3750.1-c3 |
3750.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{36} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$5.377412203$ |
$0.268374456$ |
3.332835439 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -11337\) , \( 56631\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-11337{x}+56631$ |
| 3750.1-l3 |
3750.1-l |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3750.1 |
\( 2 \cdot 3 \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{36} \) |
$2.42235$ |
$(a+1), (a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$2.765577577$ |
$0.249679047$ |
4.783971269 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -11338\) , \( -67969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-11338{x}-67969$ |
*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.
