Atkin-Lehner |
2+ 3- 5+ 17+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
34170g |
Isogeny class |
Conductor |
34170 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
1175040 |
Modular degree for the optimal curve |
Δ |
-14692474552320000 = -1 · 220 · 39 · 54 · 17 · 67 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 2 -3 4 17+ 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-9658109,11551969496] |
[a1,a2,a3,a4,a6] |
Generators |
[1731:3742:1] |
Generators of the group modulo torsion |
j |
-99632253852221316569456329/14692474552320000 |
j-invariant |
L |
5.2245171819279 |
L(r)(E,1)/r! |
Ω |
0.30854855934201 |
Real period |
R |
0.47034890581002 |
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 |
102510be1 |
Quadratic twists by: -3 |