Atkin-Lehner |
3- 5+ 29+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
69165j |
Isogeny class |
Conductor |
69165 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
63840 |
Modular degree for the optimal curve |
Δ |
-87536953125 = -1 · 36 · 57 · 29 · 53 |
Discriminant |
Eigenvalues |
1 3- 5+ -3 1 -2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,945,-9050] |
[a1,a2,a3,a4,a6] |
j |
127947874319/120078125 |
j-invariant |
L |
2.3532330621482 |
L(r)(E,1)/r! |
Ω |
0.58830826527814 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7685d1 |
Quadratic twists by: -3 |