Atkin-Lehner |
3+ 5+ 13- 83- |
Signs for the Atkin-Lehner involutions |
Class |
48555a |
Isogeny class |
Conductor |
48555 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
321408 |
Modular degree for the optimal curve |
Δ |
-96968880039378555 = -1 · 33 · 5 · 133 · 836 |
Discriminant |
Eigenvalues |
0 3+ 5+ -1 3 13- 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-275928,57764868] |
[a1,a2,a3,a4,a6] |
Generators |
[5316:380855:64] |
Generators of the group modulo torsion |
j |
-86049285226408968192/3591440001458465 |
j-invariant |
L |
4.6716852453895 |
L(r)(E,1)/r! |
Ω |
0.33450307970301 |
Real period |
R |
3.4915113857038 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000097 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
48555b2 |
Quadratic twists by: -3 |