Atkin-Lehner |
2- 3- 31- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
61752p |
Isogeny class |
Conductor |
61752 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
13440 |
Modular degree for the optimal curve |
Δ |
-17784576 = -1 · 28 · 33 · 31 · 83 |
Discriminant |
Eigenvalues |
2- 3- -3 -1 0 -1 -3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-132,576] |
[a1,a2,a3,a4,a6] |
Generators |
[6:-6:1] [0:24:1] |
Generators of the group modulo torsion |
j |
-1001132368/69471 |
j-invariant |
L |
9.8728294982274 |
L(r)(E,1)/r! |
Ω |
2.1477285898222 |
Real period |
R |
0.38307251457157 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999819 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
123504e1 |
Quadratic twists by: -4 |