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-e6 |
250.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.1 |
\( 2 \cdot 5^{3} \) |
\( 2 \cdot 5^{21} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.092166620$ |
0.891750311 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -407 a - 1088\) , \( -7693 a - 19162\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-407a-1088\right){x}-7693a-19162$ |
250.1-g6 |
250.1-g |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.1 |
\( 2 \cdot 5^{3} \) |
\( 2 \cdot 5^{21} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$4.368666483$ |
2.675250935 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 1819 a - 4474\) , \( -64789 a + 158759\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1819a-4474\right){x}-64789a+158759$ |
250.2-e6 |
250.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.2 |
\( 2 \cdot 5^{3} \) |
\( 2 \cdot 5^{21} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.368666483$ |
0.891750311 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 297 a - 848\) , \( -4565 a + 11710\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(297a-848\right){x}-4565a+11710$ |
250.2-g6 |
250.2-g |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
250.2 |
\( 2 \cdot 5^{3} \) |
\( 2 \cdot 5^{21} \) |
$1.74072$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.092166620$ |
2.675250935 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -2409 a - 5914\) , \( -102147 a - 250217\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2409a-5914\right){x}-102147a-250217$ |
450.1-d6 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.097203225$ |
$3.025641015$ |
2.710558876 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -15 a - 264\) , \( 681 a + 414\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-15a-264\right){x}+681a+414$ |
450.1-h6 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$2.628264935$ |
2.145969333 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 4549 a - 11141\) , \( -264003 a + 646669\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4549a-11141\right){x}-264003a+646669$ |
*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.