Atkin-Lehner |
2- 3- 7+ 17- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
32844d |
Isogeny class |
Conductor |
32844 |
Conductor |
∏ cp |
66 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-868853599488 = -1 · 28 · 311 · 72 · 17 · 23 |
Discriminant |
Eigenvalues |
2- 3- -4 7+ -1 -5 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3060,78084] |
[a1,a2,a3,a4,a6] |
Generators |
[-36:378:1] [-60:222:1] |
Generators of the group modulo torsion |
j |
-12381975627856/3393959373 |
j-invariant |
L |
7.9076995723199 |
L(r)(E,1)/r! |
Ω |
0.84380079572885 |
Real period |
R |
0.14199279082234 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
98532m1 |
Quadratic twists by: -3 |