Atkin-Lehner |
2- 3+ 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
89712j |
Isogeny class |
Conductor |
89712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1140480 |
Modular degree for the optimal curve |
Δ |
-246979780015030272 = -1 · 223 · 39 · 75 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 4 7+ 0 -4 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-45603,24202530] |
[a1,a2,a3,a4,a6] |
Generators |
[1585:62720:1] |
Generators of the group modulo torsion |
j |
-130092635763/3063445504 |
j-invariant |
L |
8.7472681452923 |
L(r)(E,1)/r! |
Ω |
0.26168520309606 |
Real period |
R |
4.1783352886294 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999959129 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11214b1 89712h1 |
Quadratic twists by: -4 -3 |