Atkin-Lehner |
2+ 3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
36192j |
Isogeny class |
Conductor |
36192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
11264 |
Modular degree for the optimal curve |
Δ |
81866304 = 26 · 32 · 132 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -4 0 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-254,1584] |
[a1,a2,a3,a4,a6] |
Generators |
[-16:36:1] [-5:52:1] |
Generators of the group modulo torsion |
j |
28428476608/1279161 |
j-invariant |
L |
6.0867103473665 |
L(r)(E,1)/r! |
Ω |
1.9031182657978 |
Real period |
R |
3.1982827640057 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
36192s1 72384da2 108576bp1 |
Quadratic twists by: -4 8 -3 |