Atkin-Lehner |
2+ 3+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
9048a |
Isogeny class |
Conductor |
9048 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
42240 |
Modular degree for the optimal curve |
Δ |
37815621743952 = 24 · 32 · 135 · 294 |
Discriminant |
Eigenvalues |
2+ 3+ 0 4 2 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-122923,-16544600] |
[a1,a2,a3,a4,a6] |
Generators |
[10963:1147227:1] |
Generators of the group modulo torsion |
j |
12838276213282048000/2363476358997 |
j-invariant |
L |
4.2961407460414 |
L(r)(E,1)/r! |
Ω |
0.25497392545957 |
Real period |
R |
8.4246668326929 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
18096k1 72384bj1 27144j1 117624bd1 |
Quadratic twists by: -4 8 -3 13 |