| 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 |
| 250.1-e3 |
250.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.1 |
\( 2 \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{18} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.368666483$ |
0.891750311 |
\( \frac{57960603}{31250} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -32 a - 88\) , \( -68 a - 162\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-32a-88\right){x}-68a-162$ |
| 250.1-g3 |
250.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.1 |
\( 2 \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{18} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$4.368666483$ |
2.675250935 |
\( \frac{57960603}{31250} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 194 a - 474\) , \( 711 a - 1741\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(194a-474\right){x}+711a-1741$ |
| 250.2-e3 |
250.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.2 |
\( 2 \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{18} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.368666483$ |
0.891750311 |
\( \frac{57960603}{31250} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 32 a - 88\) , \( 68 a - 162\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-88\right){x}+68a-162$ |
| 250.2-g3 |
250.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.2 |
\( 2 \cdot 5^{3} \) |
\( 2^{2} \cdot 5^{18} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$4.368666483$ |
2.675250935 |
\( \frac{57960603}{31250} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -194 a - 474\) , \( -711 a - 1741\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-194a-474\right){x}-711a-1741$ |
| 450.1-d3 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{12} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.548601612$ |
$6.051282030$ |
2.710558876 |
\( \frac{57960603}{31250} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24\) , \( 18\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-24{x}+18$ |
| 450.1-h3 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{12} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$5.256529870$ |
2.145969333 |
\( \frac{57960603}{31250} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -484 a - 1184\) , \( -3083 a - 7553\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-484a-1184\right){x}-3083a-7553$ |
*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.
