Atkin-Lehner |
3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347w |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
80640 |
Modular degree for the optimal curve |
Δ |
-2664992265507 = -1 · 33 · 112 · 138 |
Discriminant |
Eigenvalues |
0 3- 0 -1 11- 13+ -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-12393,-540952] |
[a1,a2,a3,a4,a6] |
Generators |
[654:16477:1] |
Generators of the group modulo torsion |
j |
-360448000/4563 |
j-invariant |
L |
5.4193578014832 |
L(r)(E,1)/r! |
Ω |
0.22607121471491 |
Real period |
R |
1.9976587939563 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997335 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61347v1 4719i1 |
Quadratic twists by: -11 13 |