Atkin-Lehner |
2+ 7- 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
32186f |
Isogeny class |
Conductor |
32186 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8448 |
Modular degree for the optimal curve |
Δ |
-45317888 = -1 · 28 · 7 · 113 · 19 |
Discriminant |
Eigenvalues |
2+ 0 -2 7- 11+ 0 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-28,336] |
[a1,a2,a3,a4,a6] |
Generators |
[3:15:1] [134:461:8] |
Generators of the group modulo torsion |
j |
-1860867/34048 |
j-invariant |
L |
5.6848345560615 |
L(r)(E,1)/r! |
Ω |
1.7026078934796 |
Real period |
R |
3.3388982735438 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32186o1 |
Quadratic twists by: -11 |