Atkin-Lehner |
2- 7+ 13- 37- |
Signs for the Atkin-Lehner involutions |
Class |
47138j |
Isogeny class |
Conductor |
47138 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
-4730392576 = -1 · 212 · 74 · 13 · 37 |
Discriminant |
Eigenvalues |
2- -2 -3 7+ 0 13- -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-442,4836] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:54:1] [-20:86:1] |
Generators of the group modulo torsion |
j |
-3977954113/1970176 |
j-invariant |
L |
8.400048310757 |
L(r)(E,1)/r! |
Ω |
1.2787831130883 |
Real period |
R |
1.6421956594483 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
47138n1 |
Quadratic twists by: -7 |