Atkin-Lehner |
2- 3- 5+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
111600fn |
Isogeny class |
Conductor |
111600 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
393216 |
Modular degree for the optimal curve |
Δ |
21695040000000 = 212 · 37 · 57 · 31 |
Discriminant |
Eigenvalues |
2- 3- 5+ -4 -4 -2 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-36075,-2627750] |
[a1,a2,a3,a4,a6] |
Generators |
[-106:72:1] [-105:50:1] |
Generators of the group modulo torsion |
j |
111284641/465 |
j-invariant |
L |
9.8631992130178 |
L(r)(E,1)/r! |
Ω |
0.34650311258942 |
Real period |
R |
3.5581207104398 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000003982 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6975g1 37200di1 22320bt1 |
Quadratic twists by: -4 -3 5 |