Atkin-Lehner |
2- 3+ 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
7686n |
Isogeny class |
Conductor |
7686 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
3168 |
Modular degree for the optimal curve |
Δ |
-67237128 = -1 · 23 · 39 · 7 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- -5 -1 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-191,1135] |
[a1,a2,a3,a4,a6] |
Generators |
[13:20:1] |
Generators of the group modulo torsion |
j |
-38958219/3416 |
j-invariant |
L |
5.4931543244513 |
L(r)(E,1)/r! |
Ω |
1.9132327260793 |
Real period |
R |
0.47852292523661 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61488m1 7686c1 53802bo1 |
Quadratic twists by: -4 -3 -7 |