Atkin-Lehner |
2+ 5+ 13- 79- |
Signs for the Atkin-Lehner involutions |
Class |
51350i |
Isogeny class |
Conductor |
51350 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
1710720 |
Modular degree for the optimal curve |
Δ |
-5554016000000 = -1 · 211 · 56 · 133 · 79 |
Discriminant |
Eigenvalues |
2+ 0 5+ 3 -5 13- 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-29003392,60127574016] |
[a1,a2,a3,a4,a6] |
Generators |
[388655:-190486:125] |
Generators of the group modulo torsion |
j |
-172683193545007865807697/355457024 |
j-invariant |
L |
4.6140030996255 |
L(r)(E,1)/r! |
Ω |
0.35013892243993 |
Real period |
R |
4.39254517175 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2054f1 |
Quadratic twists by: 5 |