Atkin-Lehner |
2+ 3+ 5+ 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
84150b |
Isogeny class |
Conductor |
84150 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
36479025000000 = 26 · 33 · 58 · 11 · 173 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 4 11+ -2 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-83442,9293716] |
[a1,a2,a3,a4,a6] |
Generators |
[-36:3518:1] |
Generators of the group modulo torsion |
j |
152298969481827/86468800 |
j-invariant |
L |
5.5296951456854 |
L(r)(E,1)/r! |
Ω |
0.6429566268812 |
Real period |
R |
2.1501042671646 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999953874 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
84150el3 16830bk1 |
Quadratic twists by: -3 5 |