Atkin-Lehner |
2- 3+ 5- 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
86190cg |
Isogeny class |
Conductor |
86190 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
688416768000 = 214 · 32 · 53 · 133 · 17 |
Discriminant |
Eigenvalues |
2- 3+ 5- -4 -4 13- 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-4625,112367] |
[a1,a2,a3,a4,a6] |
Generators |
[-73:296:1] [-69:364:1] |
Generators of the group modulo torsion |
j |
4980061835533/313344000 |
j-invariant |
L |
13.070347908587 |
L(r)(E,1)/r! |
Ω |
0.8903155365083 |
Real period |
R |
0.34953760432811 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000034 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86190k1 |
Quadratic twists by: 13 |