Atkin-Lehner |
2- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
31768f |
Isogeny class |
Conductor |
31768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4032 |
Modular degree for the optimal curve |
Δ |
698896 = 24 · 112 · 192 |
Discriminant |
Eigenvalues |
2- -1 3 -4 11+ -1 1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-44,121] |
[a1,a2,a3,a4,a6] |
Generators |
[0:11:1] |
Generators of the group modulo torsion |
j |
1668352/121 |
j-invariant |
L |
4.2112516462727 |
L(r)(E,1)/r! |
Ω |
2.8028230247523 |
Real period |
R |
0.37562589655876 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63536h1 31768a1 |
Quadratic twists by: -4 -19 |