Atkin-Lehner |
3- 5+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
48165r |
Isogeny class |
Conductor |
48165 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
219648 |
Modular degree for the optimal curve |
Δ |
508440879745695 = 38 · 5 · 138 · 19 |
Discriminant |
Eigenvalues |
-1 3- 5+ 3 0 13+ -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-84081,9314226] |
[a1,a2,a3,a4,a6] |
Generators |
[183:162:1] |
Generators of the group modulo torsion |
j |
80588082289/623295 |
j-invariant |
L |
4.5592814706626 |
L(r)(E,1)/r! |
Ω |
0.52517603673165 |
Real period |
R |
0.36172644597573 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999499 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48165z1 |
Quadratic twists by: 13 |