Atkin-Lehner |
3- 5+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
48165p |
Isogeny class |
Conductor |
48165 |
Conductor |
∏ cp |
45 |
Product of Tamagawa factors cp |
deg |
804960 |
Modular degree for the optimal curve |
Δ |
1111960204003834965 = 315 · 5 · 138 · 19 |
Discriminant |
Eigenvalues |
0 3- 5+ 2 6 13+ -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-301721,-38769259] |
[a1,a2,a3,a4,a6] |
Generators |
[-201592:2239961:512] |
Generators of the group modulo torsion |
j |
3723873746944/1363146165 |
j-invariant |
L |
6.883603349731 |
L(r)(E,1)/r! |
Ω |
0.20995365447228 |
Real period |
R |
6.5572598553104 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999958 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
48165v1 |
Quadratic twists by: 13 |