Atkin-Lehner |
2+ 7+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
13706c |
Isogeny class |
Conductor |
13706 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-402340834373632 = -1 · 212 · 7 · 116 · 892 |
Discriminant |
Eigenvalues |
2+ 2 2 7+ 11- 4 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-27239,1969973] |
[a1,a2,a3,a4,a6] |
Generators |
[3837:25004:27] |
Generators of the group modulo torsion |
j |
-2235229410904052473/402340834373632 |
j-invariant |
L |
5.6891651874153 |
L(r)(E,1)/r! |
Ω |
0.51211103848412 |
Real period |
R |
1.8515402454695 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
109648t1 123354bo1 95942r1 |
Quadratic twists by: -4 -3 -7 |