Atkin-Lehner |
3+ 11+ 13+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
18447b |
Isogeny class |
Conductor |
18447 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
311040 |
Modular degree for the optimal curve |
Δ |
-654940751519910141 = -1 · 316 · 115 · 133 · 43 |
Discriminant |
Eigenvalues |
-1 3+ -3 -3 11+ 13+ -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-55517,-39284008] |
[a1,a2,a3,a4,a6] |
Generators |
[2718:139702:1] |
Generators of the group modulo torsion |
j |
-18923530771213426513/654940751519910141 |
j-invariant |
L |
0.90106614667921 |
L(r)(E,1)/r! |
Ω |
0.12537486500162 |
Real period |
R |
3.5934880036263 |
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 |
55341d1 |
Quadratic twists by: -3 |