| 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 |
| 868.2-b4 |
868.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
868.2 |
\( 2^{2} \cdot 7 \cdot 31 \) |
\( 2^{2} \cdot 7^{18} \cdot 31 \) |
$0.84010$ |
$(-3a+1), (6a-5), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.497046915$ |
1.147880680 |
\( \frac{20687422086138241443}{50480821535223919} a + \frac{113695097195902805459}{100961643070447838} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 81 a - 203\) , \( 289 a + 272\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(81a-203\right){x}+289a+272$ |
| 54684.2-a2 |
54684.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54684.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{2} \cdot 3^{6} \cdot 7^{24} \cdot 31 \) |
$2.36681$ |
$(-2a+1), (-3a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$9$ |
\( 2 \) |
$1$ |
$0.108464529$ |
2.254392903 |
\( \frac{20687422086138241443}{50480821535223919} a + \frac{113695097195902805459}{100961643070447838} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 3053 a - 4156\) , \( 6565 a - 58879\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(3053a-4156\right){x}+6565a-58879$ |
| 55552.2-e2 |
55552.2-e |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
55552.2 |
\( 2^{8} \cdot 7 \cdot 31 \) |
\( 2^{26} \cdot 7^{18} \cdot 31 \) |
$2.37615$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$2.657384984$ |
$0.124261728$ |
3.050360885 |
\( \frac{20687422086138241443}{50480821535223919} a + \frac{113695097195902805459}{100961643070447838} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1301 a - 3258\) , \( -19159 a - 21954\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1301a-3258\right){x}-19159a-21954$ |
| 146692.2-b2 |
146692.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146692.2 |
\( 2^{2} \cdot 7 \cdot 13^{2} \cdot 31 \) |
\( 2^{2} \cdot 7^{18} \cdot 13^{6} \cdot 31 \) |
$3.02901$ |
$(-3a+1), (-4a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.252641283$ |
$0.137856010$ |
2.895555473 |
\( \frac{20687422086138241443}{50480821535223919} a + \frac{113695097195902805459}{100961643070447838} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -206 a - 2199\) , \( 27717 a - 3795\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-206a-2199\right){x}+27717a-3795$ |
| 146692.6-b2 |
146692.6-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
146692.6 |
\( 2^{2} \cdot 7 \cdot 13^{2} \cdot 31 \) |
\( 2^{2} \cdot 7^{18} \cdot 13^{6} \cdot 31 \) |
$3.02901$ |
$(-3a+1), (4a-3), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$4.988945552$ |
$0.137856010$ |
3.176609500 |
\( \frac{20687422086138241443}{50480821535223919} a + \frac{113695097195902805459}{100961643070447838} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 2075 a - 2485\) , \( -9022 a + 29784\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2075a-2485\right){x}-9022a+29784$ |
*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.
