Atkin-Lehner |
3- 7+ 11- 101+ |
Signs for the Atkin-Lehner involutions |
Class |
69993g |
Isogeny class |
Conductor |
69993 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
191488 |
Modular degree for the optimal curve |
Δ |
122665672275993 = 37 · 72 · 11 · 1014 |
Discriminant |
Eigenvalues |
1 3- 2 7+ 11- -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-30906,2029999] |
[a1,a2,a3,a4,a6] |
Generators |
[-190:1103:1] |
Generators of the group modulo torsion |
j |
4478499075397537/168265668417 |
j-invariant |
L |
7.8044125732888 |
L(r)(E,1)/r! |
Ω |
0.58362136682086 |
Real period |
R |
3.3430975185364 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000071 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23331a1 |
Quadratic twists by: -3 |