Atkin-Lehner |
2+ 3- 5- 17+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
111690q |
Isogeny class |
Conductor |
111690 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1916928 |
Modular degree for the optimal curve |
Δ |
-592415254241280000 = -1 · 216 · 37 · 54 · 17 · 733 |
Discriminant |
Eigenvalues |
2+ 3- 5- 3 2 2 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-67284,37652688] |
[a1,a2,a3,a4,a6] |
Generators |
[72:-5796:1] |
Generators of the group modulo torsion |
j |
-46209920460234049/812640952320000 |
j-invariant |
L |
7.0784140518047 |
L(r)(E,1)/r! |
Ω |
0.24457248265318 |
Real period |
R |
0.90443714702863 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000030124 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
37230bb1 |
Quadratic twists by: -3 |