Atkin-Lehner |
2+ 3+ 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
128064m |
Isogeny class |
Conductor |
128064 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-302140882944 = -1 · 224 · 33 · 23 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -4 -3 -5 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5889,177921] |
[a1,a2,a3,a4,a6] |
Generators |
[35:116:1] [65:256:1] |
Generators of the group modulo torsion |
j |
-86175179713/1152576 |
j-invariant |
L |
10.338408753205 |
L(r)(E,1)/r! |
Ω |
0.97345268365148 |
Real period |
R |
2.6550876395587 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000094 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128064dw1 4002m1 |
Quadratic twists by: -4 8 |