Atkin-Lehner |
3+ 5+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
42075m |
Isogeny class |
Conductor |
42075 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
768000 |
Modular degree for the optimal curve |
Δ |
3916996799331515625 = 33 · 56 · 113 · 178 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 2 11- 2 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2090105,-1158627728] |
[a1,a2,a3,a4,a6] |
Generators |
[-830:2378:1] |
Generators of the group modulo torsion |
j |
2393558463315519963/9284733153971 |
j-invariant |
L |
4.4293143995542 |
L(r)(E,1)/r! |
Ω |
0.12559110252232 |
Real period |
R |
1.4694891830836 |
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 |
42075a1 1683c1 |
Quadratic twists by: -3 5 |