Atkin-Lehner |
2+ 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264j |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
49920 |
Modular degree for the optimal curve |
Δ |
1166959872 = 28 · 36 · 132 · 37 |
Discriminant |
Eigenvalues |
2+ 3- 0 -3 -5 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3540,81052] |
[a1,a2,a3,a4,a6] |
Generators |
[33:13:1] |
Generators of the group modulo torsion |
j |
26288512000/6253 |
j-invariant |
L |
3.4654211446652 |
L(r)(E,1)/r! |
Ω |
1.5023976735713 |
Real period |
R |
1.153296894937 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002553 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34632d1 7696a1 |
Quadratic twists by: -4 -3 |