Atkin-Lehner |
2+ 3- 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384bd |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1575936 |
Modular degree for the optimal curve |
Δ |
-236429497149161472 = -1 · 237 · 33 · 133 · 29 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 -3 13+ 5 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3329217,2337097887] |
[a1,a2,a3,a4,a6] |
Generators |
[1074:1227:1] |
Generators of the group modulo torsion |
j |
-15567190192349720497/901906956288 |
j-invariant |
L |
8.494793346922 |
L(r)(E,1)/r! |
Ω |
0.29642234234504 |
Real period |
R |
4.7762893978143 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000959 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384bv1 2262i1 |
Quadratic twists by: -4 8 |