Atkin-Lehner |
2+ 3+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384c |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-110662382518272 = -1 · 227 · 37 · 13 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 1 13+ -7 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-17857,1054657] |
[a1,a2,a3,a4,a6] |
Generators |
[48:553:1] |
Generators of the group modulo torsion |
j |
-2402335209457/422143488 |
j-invariant |
L |
5.413651656514 |
L(r)(E,1)/r! |
Ω |
0.57064386897793 |
Real period |
R |
4.7434590555173 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001767 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384cu1 2262l1 |
Quadratic twists by: -4 8 |