Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232bi |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-424030464 = -1 · 28 · 34 · 112 · 132 |
Discriminant |
Eigenvalues |
2- 3+ -1 2 11- 13+ 1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-316,-2276] |
[a1,a2,a3,a4,a6] |
Generators |
[170:99:8] |
Generators of the group modulo torsion |
j |
-80915536/9801 |
j-invariant |
L |
5.702576748355 |
L(r)(E,1)/r! |
Ω |
0.56220470757965 |
Real period |
R |
2.535809763458 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003831 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22308c1 89232bb1 |
Quadratic twists by: -4 13 |