Atkin-Lehner |
2+ 3- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
8184i |
Isogeny class |
Conductor |
8184 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
5376 |
Modular degree for the optimal curve |
Δ |
-31894963056 = -1 · 24 · 312 · 112 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 1 -1 11+ 6 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,340,8361] |
[a1,a2,a3,a4,a6] |
Generators |
[4:99:1] |
Generators of the group modulo torsion |
j |
270871003904/1993435191 |
j-invariant |
L |
5.3848930597643 |
L(r)(E,1)/r! |
Ω |
0.85230284684918 |
Real period |
R |
0.13162606753357 |
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 |
16368c1 65472k1 24552w1 90024be1 |
Quadratic twists by: -4 8 -3 -11 |