Atkin-Lehner |
2+ 3+ 7- 29- |
Signs for the Atkin-Lehner involutions |
Class |
68208n |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
134400 |
Modular degree for the optimal curve |
Δ |
1739929330944 = 28 · 314 · 72 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- 4 -3 8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4097,-77139] |
[a1,a2,a3,a4,a6] |
Generators |
[1364:50301:1] |
Generators of the group modulo torsion |
j |
606445192192/138706101 |
j-invariant |
L |
4.1225735568678 |
L(r)(E,1)/r! |
Ω |
0.60653116940025 |
Real period |
R |
3.3984845016025 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999975177 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34104z1 68208p1 |
Quadratic twists by: -4 -7 |