Atkin-Lehner |
2+ 3- 7+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
68208p |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
940800 |
Modular degree for the optimal curve |
Δ |
204700945856230656 = 28 · 314 · 78 · 29 |
Discriminant |
Eigenvalues |
2+ 3- 3 7+ 4 3 -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-200769,26860203] |
[a1,a2,a3,a4,a6] |
Generators |
[-474:3969:1] |
Generators of the group modulo torsion |
j |
606445192192/138706101 |
j-invariant |
L |
10.840609088029 |
L(r)(E,1)/r! |
Ω |
0.29847935038358 |
Real period |
R |
0.8647490684684 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996089 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34104u1 68208n1 |
Quadratic twists by: -4 -7 |