Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232bm |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-373190028017664 = -1 · 214 · 3 · 112 · 137 |
Discriminant |
Eigenvalues |
2- 3+ 2 4 11- 13+ 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-17632,1300480] |
[a1,a2,a3,a4,a6] |
Generators |
[165:1690:1] |
Generators of the group modulo torsion |
j |
-30664297/18876 |
j-invariant |
L |
8.3824744931797 |
L(r)(E,1)/r! |
Ω |
0.4961334706828 |
Real period |
R |
2.1119504572257 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000013303 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11154bd1 6864n1 |
Quadratic twists by: -4 13 |