Atkin-Lehner |
5+ 23- 79- |
Signs for the Atkin-Lehner involutions |
Class |
9085d |
Isogeny class |
Conductor |
9085 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
84864 |
Modular degree for the optimal curve |
Δ |
-31884002685546875 = -1 · 517 · 232 · 79 |
Discriminant |
Eigenvalues |
0 -1 5+ 5 -1 -4 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-221531,41115987] |
[a1,a2,a3,a4,a6] |
Generators |
[285:1023:1] |
Generators of the group modulo torsion |
j |
-1202345262001752408064/31884002685546875 |
j-invariant |
L |
2.8823637111123 |
L(r)(E,1)/r! |
Ω |
0.36916899542926 |
Real period |
R |
3.9038539893643 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81765i1 45425b1 |
Quadratic twists by: -3 5 |