Atkin-Lehner |
2- 3- 11- 59- |
Signs for the Atkin-Lehner involutions |
Class |
42834bj |
Isogeny class |
Conductor |
42834 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
21854316635712 = 26 · 33 · 118 · 59 |
Discriminant |
Eigenvalues |
2- 3- -4 0 11- -2 8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-7565,-117039] |
[a1,a2,a3,a4,a6] |
Generators |
[-56:391:1] |
Generators of the group modulo torsion |
j |
27027009001/12336192 |
j-invariant |
L |
8.2501849017662 |
L(r)(E,1)/r! |
Ω |
0.53454445312385 |
Real period |
R |
0.85744712712763 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128502s1 3894e1 |
Quadratic twists by: -3 -11 |