Atkin-Lehner |
2+ 3+ 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312q |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
168960 |
Modular degree for the optimal curve |
Δ |
569335430976 = 26 · 3 · 134 · 473 |
Discriminant |
Eigenvalues |
2+ 3+ -1 5 -3 13- 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2711,-39531] |
[a1,a2,a3,a4,a6] |
Generators |
[-310:611:8] |
Generators of the group modulo torsion |
j |
34442326406656/8895866109 |
j-invariant |
L |
6.4508780219754 |
L(r)(E,1)/r! |
Ω |
0.67425224072655 |
Real period |
R |
0.79728791764674 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000065488 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312bf1 58656u1 |
Quadratic twists by: -4 8 |