Atkin-Lehner |
11+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
4147b |
Isogeny class |
Conductor |
4147 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4416 |
Modular degree for the optimal curve |
Δ |
-31970355131 = -1 · 113 · 134 · 292 |
Discriminant |
Eigenvalues |
-2 1 -3 0 11+ 13- 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,58,8620] |
[a1,a2,a3,a4,a6] |
Generators |
[29:188:1] |
Generators of the group modulo torsion |
j |
21207928832/31970355131 |
j-invariant |
L |
1.7107115554429 |
L(r)(E,1)/r! |
Ω |
0.91621463461737 |
Real period |
R |
0.23339394106018 |
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 |
66352r1 37323l1 103675g1 45617b1 |
Quadratic twists by: -4 -3 5 -11 |