Atkin-Lehner |
2- 3+ 7+ 101+ |
Signs for the Atkin-Lehner involutions |
Class |
8484a |
Isogeny class |
Conductor |
8484 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
4224 |
Modular degree for the optimal curve |
Δ |
102622464 = 28 · 34 · 72 · 101 |
Discriminant |
Eigenvalues |
2- 3+ -3 7+ 0 -5 -7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-117,81] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:18:1] [-8:21:1] |
Generators of the group modulo torsion |
j |
697827328/400869 |
j-invariant |
L |
4.2990467996302 |
L(r)(E,1)/r! |
Ω |
1.6122473713076 |
Real period |
R |
0.22220777428136 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999982 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33936i1 25452c1 59388c1 |
Quadratic twists by: -4 -3 -7 |