Atkin-Lehner |
2+ 3+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
8184a |
Isogeny class |
Conductor |
8184 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4224 |
Modular degree for the optimal curve |
Δ |
982341888 = 28 · 3 · 113 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 11+ 0 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1372,-19052] |
[a1,a2,a3,a4,a6] |
Generators |
[1731:10540:27] |
Generators of the group modulo torsion |
j |
1116509913808/3837273 |
j-invariant |
L |
3.8636867904846 |
L(r)(E,1)/r! |
Ω |
0.78455682232975 |
Real period |
R |
4.9246742626127 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16368m1 65472bd1 24552t1 90024s1 |
Quadratic twists by: -4 8 -3 -11 |