Atkin-Lehner |
2+ 7+ 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
33418c |
Isogeny class |
Conductor |
33418 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
126336 |
Modular degree for the optimal curve |
Δ |
117126125255062 = 2 · 78 · 11 · 314 |
Discriminant |
Eigenvalues |
2+ -1 -2 7+ 11+ -5 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-39666,2979334] |
[a1,a2,a3,a4,a6] |
Generators |
[-225:872:1] [69:725:1] |
Generators of the group modulo torsion |
j |
1197324094057/20317462 |
j-invariant |
L |
4.6464687465751 |
L(r)(E,1)/r! |
Ω |
0.5913177873853 |
Real period |
R |
0.65481833481357 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33418h1 |
Quadratic twists by: -7 |