Atkin-Lehner |
2- 3+ 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
89712l |
Isogeny class |
Conductor |
89712 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
211968 |
Modular degree for the optimal curve |
Δ |
-56741137625088 = -1 · 212 · 33 · 78 · 89 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 6 4 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-96,362416] |
[a1,a2,a3,a4,a6] |
Generators |
[89:1029:1] |
Generators of the group modulo torsion |
j |
-884736/513067289 |
j-invariant |
L |
6.4726092537406 |
L(r)(E,1)/r! |
Ω |
0.4991499834657 |
Real period |
R |
0.81045395557881 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999958449 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5607a1 89712n1 |
Quadratic twists by: -4 -3 |