Atkin-Lehner |
2- 3+ 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
48576bw |
Isogeny class |
Conductor |
48576 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-1680875716608 = -1 · 226 · 32 · 112 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 11+ -2 -8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2687,31009] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:132:1] [16:279:1] |
Generators of the group modulo torsion |
j |
8181353375/6412032 |
j-invariant |
L |
8.5629693091772 |
L(r)(E,1)/r! |
Ω |
0.54045855257058 |
Real period |
R |
3.9609740971109 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
48576br1 12144bk1 |
Quadratic twists by: -4 8 |