Atkin-Lehner |
2+ 3+ 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
34056a |
Isogeny class |
Conductor |
34056 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
217728 |
Modular degree for the optimal curve |
Δ |
-31931101268543664 = -1 · 24 · 39 · 119 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -1 11- -6 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-32778,8895609] |
[a1,a2,a3,a4,a6] |
Generators |
[-248:1331:1] [60:2673:1] |
Generators of the group modulo torsion |
j |
-12366869833728/101391750713 |
j-invariant |
L |
7.978968161759 |
L(r)(E,1)/r! |
Ω |
0.31700744158161 |
Real period |
R |
0.69915710302409 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68112a1 34056n1 |
Quadratic twists by: -4 -3 |