Atkin-Lehner |
3+ 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
15609i |
Isogeny class |
Conductor |
15609 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
76032 |
Modular degree for the optimal curve |
Δ |
-1351475966907 = -1 · 33 · 114 · 434 |
Discriminant |
Eigenvalues |
-2 3+ 0 5 11- 6 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-23998,-1424028] |
[a1,a2,a3,a4,a6] |
Generators |
[180:236:1] |
Generators of the group modulo torsion |
j |
-104398970368000/92307627 |
j-invariant |
L |
2.7056174818107 |
L(r)(E,1)/r! |
Ω |
0.19177909366976 |
Real period |
R |
1.175665809916 |
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 |
46827t1 15609e1 |
Quadratic twists by: -3 -11 |