Atkin-Lehner |
2+ 3+ 7+ 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
85008a |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
175104 |
Modular degree for the optimal curve |
Δ |
12754898613072 = 24 · 312 · 72 · 113 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ 11+ 0 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8503,250954] |
[a1,a2,a3,a4,a6] |
Generators |
[804:24451:64] |
Generators of the group modulo torsion |
j |
4249827878656000/797181163317 |
j-invariant |
L |
4.229839861563 |
L(r)(E,1)/r! |
Ω |
0.67499517887562 |
Real period |
R |
6.2664741741075 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000012984 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42504j1 |
Quadratic twists by: -4 |