Atkin-Lehner |
2+ 3+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384u |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
101376 |
Modular degree for the optimal curve |
Δ |
-1122046967808 = -1 · 217 · 33 · 13 · 293 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 5 13- 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2431,20865] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:29:1] |
Generators of the group modulo torsion |
j |
12116857534/8560539 |
j-invariant |
L |
5.6200292388534 |
L(r)(E,1)/r! |
Ω |
0.55126932347883 |
Real period |
R |
1.6991178360098 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999983024 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384dw1 9048l1 |
Quadratic twists by: -4 8 |