Atkin-Lehner |
2- 3+ 19+ 79+ |
Signs for the Atkin-Lehner involutions |
Class |
72048j |
Isogeny class |
Conductor |
72048 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
8256 |
Modular degree for the optimal curve |
Δ |
-72048 = -1 · 24 · 3 · 19 · 79 |
Discriminant |
Eigenvalues |
2- 3+ -4 -4 -2 -4 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,10,-9] |
[a1,a2,a3,a4,a6] |
Generators |
[1:1:1] [9:27:1] |
Generators of the group modulo torsion |
j |
6243584/4503 |
j-invariant |
L |
5.3158503586166 |
L(r)(E,1)/r! |
Ω |
1.9438107913482 |
Real period |
R |
2.7347570979052 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999857 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
18012i1 |
Quadratic twists by: -4 |