Atkin-Lehner |
2- 3- 7- 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
72618ci |
Isogeny class |
Conductor |
72618 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
12917673843984 = 24 · 34 · 79 · 13 · 19 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 4 13- -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-87074,9880884] |
[a1,a2,a3,a4,a6] |
Generators |
[-20:3418:1] |
Generators of the group modulo torsion |
j |
620584994493073/109798416 |
j-invariant |
L |
11.08620803241 |
L(r)(E,1)/r! |
Ω |
0.68771704806129 |
Real period |
R |
4.0300760549338 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000508 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
10374j1 |
Quadratic twists by: -7 |