Atkin-Lehner |
2+ 5- 7- |
Signs for the Atkin-Lehner involutions |
Class |
78400ew |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-6588344000 = -1 · 26 · 53 · 77 |
Discriminant |
Eigenvalues |
2+ -1 5- 7- 3 -1 7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,327,3067] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:49:1] |
Generators of the group modulo torsion |
j |
4096/7 |
j-invariant |
L |
5.3875197681033 |
L(r)(E,1)/r! |
Ω |
0.91372339245939 |
Real period |
R |
0.73702826970508 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001181 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78400kj1 1225j1 78400ej1 11200bo1 |
Quadratic twists by: -4 8 5 -7 |