Atkin-Lehner |
5+ 29+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
10585a |
Isogeny class |
Conductor |
10585 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
772705 = 5 · 29 · 732 |
Discriminant |
Eigenvalues |
-1 0 5+ -2 2 2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-16098,-782104] |
[a1,a2,a3,a4,a6] |
j |
461332646708918769/772705 |
j-invariant |
L |
0.84769315696222 |
L(r)(E,1)/r! |
Ω |
0.42384657848111 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
95265i1 52925a1 |
Quadratic twists by: -3 5 |