Atkin-Lehner |
2- 3+ 7+ 11+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
40194z |
Isogeny class |
Conductor |
40194 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-297114048 = -1 · 26 · 33 · 72 · 112 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -4 7+ 11+ -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,163,165] |
[a1,a2,a3,a4,a6] |
Generators |
[5:-36:1] |
Generators of the group modulo torsion |
j |
17840960397/11004224 |
j-invariant |
L |
5.6611136484788 |
L(r)(E,1)/r! |
Ω |
1.0670190015206 |
Real period |
R |
0.44212846259898 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000008 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
40194b1 |
Quadratic twists by: -3 |