Atkin-Lehner |
2+ 3- 31+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69936d |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
116736 |
Modular degree for the optimal curve |
Δ |
-582280771824 = -1 · 24 · 312 · 31 · 472 |
Discriminant |
Eigenvalues |
2+ 3- -1 -5 -2 -2 6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1556,43143] |
[a1,a2,a3,a4,a6] |
Generators |
[61:-423:1] [13:159:1] |
Generators of the group modulo torsion |
j |
-26056230479104/36392548239 |
j-invariant |
L |
10.151213904971 |
L(r)(E,1)/r! |
Ω |
0.82740263360449 |
Real period |
R |
0.5111988152612 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999493 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34968g1 |
Quadratic twists by: -4 |