Atkin-Lehner |
2- 13- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
34528d |
Isogeny class |
Conductor |
34528 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
47360 |
Modular degree for the optimal curve |
Δ |
-1309612788224 = -1 · 29 · 135 · 832 |
Discriminant |
Eigenvalues |
2- -1 3 -3 2 13- 5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1344,-57788] |
[a1,a2,a3,a4,a6] |
Generators |
[64:338:1] |
Generators of the group modulo torsion |
j |
-524776831496/2557837477 |
j-invariant |
L |
5.3450561409365 |
L(r)(E,1)/r! |
Ω |
0.35634941094184 |
Real period |
R |
0.74997403907719 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34528a1 69056d1 |
Quadratic twists by: -4 8 |