Atkin-Lehner |
3+ 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
89739b |
Isogeny class |
Conductor |
89739 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
548352 |
Modular degree for the optimal curve |
Δ |
72869664546549 = 39 · 137 · 59 |
Discriminant |
Eigenvalues |
-2 3+ -3 4 -2 13+ -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-13689,459722] |
[a1,a2,a3,a4,a6] |
Generators |
[195:-2282:1] |
Generators of the group modulo torsion |
j |
2985984/767 |
j-invariant |
L |
2.7176391400462 |
L(r)(E,1)/r! |
Ω |
0.5750438472996 |
Real period |
R |
1.181492144283 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999530301 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89739d1 6903d1 |
Quadratic twists by: -3 13 |