Atkin-Lehner |
2+ 7- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
32186n |
Isogeny class |
Conductor |
32186 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
65664 |
Modular degree for the optimal curve |
Δ |
-2487288568996 = -1 · 22 · 76 · 114 · 192 |
Discriminant |
Eigenvalues |
2+ -2 -3 7- 11- -1 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-3270,104300] |
[a1,a2,a3,a4,a6] |
Generators |
[-67:187:1] [43:187:1] |
Generators of the group modulo torsion |
j |
-264000833833/169885156 |
j-invariant |
L |
3.8801273824006 |
L(r)(E,1)/r! |
Ω |
0.75215809653339 |
Real period |
R |
0.64483241626372 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
32186r1 |
Quadratic twists by: -11 |