Atkin-Lehner |
3- 5+ 7+ 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
42315d |
Isogeny class |
Conductor |
42315 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
51200 |
Modular degree for the optimal curve |
Δ |
12550417425 = 34 · 52 · 7 · 134 · 31 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ 0 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-9211,-340984] |
[a1,a2,a3,a4,a6] |
Generators |
[-55:29:1] |
Generators of the group modulo torsion |
j |
86426515936112689/12550417425 |
j-invariant |
L |
3.3879090854306 |
L(r)(E,1)/r! |
Ω |
0.48733364746071 |
Real period |
R |
1.7379823366852 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999829 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126945p1 |
Quadratic twists by: -3 |