Atkin-Lehner |
2- 5+ 7- |
Signs for the Atkin-Lehner involutions |
Class |
78400gz |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
-210827008000000 = -1 · 214 · 56 · 77 |
Discriminant |
Eigenvalues |
2- 0 5+ 7- -4 -2 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,4900,686000] |
[a1,a2,a3,a4,a6] |
Generators |
[-14:784:1] |
Generators of the group modulo torsion |
j |
432/7 |
j-invariant |
L |
3.7304208756721 |
L(r)(E,1)/r! |
Ω |
0.41811406614523 |
Real period |
R |
1.1152521461196 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999997164 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78400u1 19600h1 3136s1 11200bv1 |
Quadratic twists by: -4 8 5 -7 |