Atkin-Lehner |
2+ 7+ 17- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
81872d |
Isogeny class |
Conductor |
81872 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
26112 |
Modular degree for the optimal curve |
Δ |
-36678656 = -1 · 210 · 72 · 17 · 43 |
Discriminant |
Eigenvalues |
2+ -1 -3 7+ 0 -3 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-392,3136] |
[a1,a2,a3,a4,a6] |
Generators |
[14:-14:1] [-4:68:1] |
Generators of the group modulo torsion |
j |
-6522128932/35819 |
j-invariant |
L |
6.802016870131 |
L(r)(E,1)/r! |
Ω |
2.0679186929775 |
Real period |
R |
0.41116322012075 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000163 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40936m1 |
Quadratic twists by: -4 |