Atkin-Lehner |
11- 19+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
85063f |
Isogeny class |
Conductor |
85063 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
144000 |
Modular degree for the optimal curve |
Δ |
13699481213 = 117 · 19 · 37 |
Discriminant |
Eigenvalues |
2 -2 2 -2 11- 2 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-6332,-195981] |
[a1,a2,a3,a4,a6] |
Generators |
[-374:53:8] |
Generators of the group modulo torsion |
j |
15851081728/7733 |
j-invariant |
L |
8.7068547355281 |
L(r)(E,1)/r! |
Ω |
0.53520643799864 |
Real period |
R |
4.0670543723026 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000621 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7733b1 |
Quadratic twists by: -11 |