Atkin-Lehner |
2- 3+ 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
32016p |
Isogeny class |
Conductor |
32016 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
393984 |
Modular degree for the optimal curve |
Δ |
-648447511593222144 = -1 · 231 · 39 · 232 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -1 3 0 -2 5 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-443296,-119879936] |
[a1,a2,a3,a4,a6] |
Generators |
[7280112:37965824:9261] |
Generators of the group modulo torsion |
j |
-2352048005459422369/158312380760064 |
j-invariant |
L |
5.0953793175041 |
L(r)(E,1)/r! |
Ω |
0.092153620676733 |
Real period |
R |
6.9115289232341 |
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 |
4002r1 128064cz1 96048bh1 |
Quadratic twists by: -4 8 -3 |