Atkin-Lehner |
2- 3+ 23- 61- |
Signs for the Atkin-Lehner involutions |
Class |
67344n |
Isogeny class |
Conductor |
67344 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
13440 |
Modular degree for the optimal curve |
Δ |
-51720192 = -1 · 212 · 32 · 23 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 0 3 1 -1 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,27,333] |
[a1,a2,a3,a4,a6] |
j |
512000/12627 |
j-invariant |
L |
2.9993641686494 |
L(r)(E,1)/r! |
Ω |
1.4996820887267 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4209b1 |
Quadratic twists by: -4 |