Atkin-Lehner |
2- 3+ 29+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
123192g |
Isogeny class |
Conductor |
123192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
-26736791671152 = -1 · 24 · 39 · 293 · 592 |
Discriminant |
Eigenvalues |
2- 3+ 2 -5 3 -5 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-13419,-647973] |
[a1,a2,a3,a4,a6] |
Generators |
[141:513:1] |
Generators of the group modulo torsion |
j |
-848541125376/84898109 |
j-invariant |
L |
5.9073437079609 |
L(r)(E,1)/r! |
Ω |
0.22053797368717 |
Real period |
R |
3.3482576392055 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000113244 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
123192a1 |
Quadratic twists by: -3 |