Atkin-Lehner |
2+ 3+ 5+ 7- 41- |
Signs for the Atkin-Lehner involutions |
Class |
34440c |
Isogeny class |
Conductor |
34440 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
99840 |
Modular degree for the optimal curve |
Δ |
73228050000 = 24 · 36 · 55 · 72 · 41 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7- 6 -6 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-42771,3418920] |
[a1,a2,a3,a4,a6] |
Generators |
[-69:2457:1] |
Generators of the group modulo torsion |
j |
540831646674724864/4576753125 |
j-invariant |
L |
4.7654091556808 |
L(r)(E,1)/r! |
Ω |
0.98209964230977 |
Real period |
R |
2.4261332304699 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68880t1 103320bp1 |
Quadratic twists by: -4 -3 |