Atkin-Lehner |
2- 3- 5+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
67860p |
Isogeny class |
Conductor |
67860 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
699840 |
Modular degree for the optimal curve |
Δ |
23223388500000000 = 28 · 36 · 59 · 133 · 29 |
Discriminant |
Eigenvalues |
2- 3- 5+ 5 0 13- 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-205968,35223892] |
[a1,a2,a3,a4,a6] |
Generators |
[9156:188617:64] |
Generators of the group modulo torsion |
j |
5177921645510656/124439453125 |
j-invariant |
L |
7.726536797525 |
L(r)(E,1)/r! |
Ω |
0.3792676360669 |
Real period |
R |
6.7907514925833 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000512 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7540g1 |
Quadratic twists by: -3 |