Atkin-Lehner |
3- 17- 89- |
Signs for the Atkin-Lehner involutions |
Class |
13617f |
Isogeny class |
Conductor |
13617 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
-8606529531 = -1 · 39 · 173 · 89 |
Discriminant |
Eigenvalues |
-2 3- -2 -1 -1 -4 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,159,4396] |
[a1,a2,a3,a4,a6] |
Generators |
[-40488:-561644:9261] [1:67:1] |
Generators of the group modulo torsion |
j |
609800192/11805939 |
j-invariant |
L |
3.1757814756537 |
L(r)(E,1)/r! |
Ω |
0.97444018197817 |
Real period |
R |
0.27159025376737 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999965 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4539a1 |
Quadratic twists by: -3 |