Atkin-Lehner |
2- 3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
84084p |
Isogeny class |
Conductor |
84084 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
273024 |
Modular degree for the optimal curve |
Δ |
-70097873733888 = -1 · 28 · 3 · 74 · 113 · 134 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 11+ 13+ 5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-12364,660932] |
[a1,a2,a3,a4,a6] |
Generators |
[-92:1014:1] |
Generators of the group modulo torsion |
j |
-340097704912/114044073 |
j-invariant |
L |
5.922065810206 |
L(r)(E,1)/r! |
Ω |
0.58164163933813 |
Real period |
R |
1.696940009438 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999941204 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84084i1 |
Quadratic twists by: -7 |