Atkin-Lehner |
3- 7+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
48279m |
Isogeny class |
Conductor |
48279 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
84480 |
Modular degree for the optimal curve |
Δ |
-17004758747823 = -1 · 38 · 7 · 117 · 19 |
Discriminant |
Eigenvalues |
-1 3- -2 7+ 11- 2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,421,198408] |
[a1,a2,a3,a4,a6] |
Generators |
[-47:298:1] |
Generators of the group modulo torsion |
j |
4657463/9598743 |
j-invariant |
L |
3.1865036517079 |
L(r)(E,1)/r! |
Ω |
0.54382408643638 |
Real period |
R |
2.9297191235132 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999639 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
4389i1 |
Quadratic twists by: -11 |