Atkin-Lehner |
2- 3- 23- 83- |
Signs for the Atkin-Lehner involutions |
Class |
68724j |
Isogeny class |
Conductor |
68724 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
101376 |
Modular degree for the optimal curve |
Δ |
259717342464 = 28 · 312 · 23 · 83 |
Discriminant |
Eigenvalues |
2- 3- -3 0 2 4 4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-17184,-866684] |
[a1,a2,a3,a4,a6] |
Generators |
[-76:18:1] |
Generators of the group modulo torsion |
j |
3006969413632/1391661 |
j-invariant |
L |
5.7190580418062 |
L(r)(E,1)/r! |
Ω |
0.41699471620424 |
Real period |
R |
1.1429117721857 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000129 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22908d1 |
Quadratic twists by: -3 |