Atkin-Lehner |
7- 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
5551b |
Isogeny class |
Conductor |
5551 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1168 |
Modular degree for the optimal curve |
Δ |
-72163 = -1 · 7 · 132 · 61 |
Discriminant |
Eigenvalues |
2 0 -2 7- 6 13- -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-131,577] |
[a1,a2,a3,a4,a6] |
Generators |
[50:9:8] |
Generators of the group modulo torsion |
j |
-248620879872/72163 |
j-invariant |
L |
6.8414533943804 |
L(r)(E,1)/r! |
Ω |
3.3807224673877 |
Real period |
R |
1.0118330416615 |
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 |
88816i1 49959i1 38857b1 72163b1 |
Quadratic twists by: -4 -3 -7 13 |