Atkin-Lehner |
2+ 3+ 23- 29- |
Signs for the Atkin-Lehner involutions |
Class |
128064u |
Isogeny class |
Conductor |
128064 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
2359296 |
Modular degree for the optimal curve |
Δ |
-4505359273257074688 = -1 · 226 · 38 · 233 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 -2 6 -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-785569,287054113] |
[a1,a2,a3,a4,a6] |
Generators |
[-519:23552:1] |
Generators of the group modulo torsion |
j |
-204520739414888233/17186581700352 |
j-invariant |
L |
4.5245605662988 |
L(r)(E,1)/r! |
Ω |
0.23987487544366 |
Real period |
R |
1.5718474666888 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999620688 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128064dc1 4002f1 |
Quadratic twists by: -4 8 |