Atkin-Lehner |
2- 3- 7+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
69384y |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-26436969216 = -1 · 28 · 36 · 74 · 59 |
Discriminant |
Eigenvalues |
2- 3- -3 7+ -4 0 -1 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2172,39024] |
[a1,a2,a3,a4,a6] |
Generators |
[30:-42:1] [-40:252:1] |
Generators of the group modulo torsion |
j |
-1844467408/43011 |
j-invariant |
L |
10.125979364014 |
L(r)(E,1)/r! |
Ω |
1.1873981319024 |
Real period |
R |
0.11844266762716 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999963 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69384u1 |
Quadratic twists by: -7 |