Atkin-Lehner |
2+ 5- 7- |
Signs for the Atkin-Lehner involutions |
Class |
78400ed |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-3211264000 = -1 · 219 · 53 · 72 |
Discriminant |
Eigenvalues |
2+ 0 5- 7- -3 5 -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-140,2800] |
[a1,a2,a3,a4,a6] |
Generators |
[30:160:1] |
Generators of the group modulo torsion |
j |
-189/2 |
j-invariant |
L |
5.7587793545521 |
L(r)(E,1)/r! |
Ω |
1.2070004251814 |
Real period |
R |
0.59639367476689 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004166 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78400kc1 2450o1 78400ee1 78400do1 |
Quadratic twists by: -4 8 5 -7 |