Atkin-Lehner |
2- 3- 5+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970co |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
108 |
Product of Tamagawa factors cp |
deg |
304128 |
Modular degree for the optimal curve |
Δ |
-593816972146200 = -1 · 23 · 36 · 52 · 118 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5+ -1 11- -1 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,11674,1068156] |
[a1,a2,a3,a4,a6] |
Generators |
[-162:7341:8] |
Generators of the group modulo torsion |
j |
820803071/2770200 |
j-invariant |
L |
10.82135479803 |
L(r)(E,1)/r! |
Ω |
0.36527691767264 |
Real period |
R |
2.4687559571918 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997067 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
68970t1 |
Quadratic twists by: -11 |