Atkin-Lehner |
2+ 3+ 5- 43- |
Signs for the Atkin-Lehner involutions |
Class |
123840w |
Isogeny class |
Conductor |
123840 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
131072 |
Modular degree for the optimal curve |
Δ |
1857600000000 = 212 · 33 · 58 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 2 2 -2 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5172,-127264] |
[a1,a2,a3,a4,a6] |
Generators |
[-43:125:1] |
Generators of the group modulo torsion |
j |
138348848448/16796875 |
j-invariant |
L |
8.6930665291799 |
L(r)(E,1)/r! |
Ω |
0.56744573793399 |
Real period |
R |
0.95747773037201 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000014861 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
123840t1 61920b1 123840i1 |
Quadratic twists by: -4 8 -3 |