Atkin-Lehner |
2+ 3- 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
81984t |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
52 |
Product of Tamagawa factors cp |
deg |
479232 |
Modular degree for the optimal curve |
Δ |
-34978419314786304 = -1 · 220 · 313 · 73 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -1 7+ -2 -4 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,81759,86463] |
[a1,a2,a3,a4,a6] |
Generators |
[3:576:1] [579:15552:1] |
Generators of the group modulo torsion |
j |
230560651724759/133432080516 |
j-invariant |
L |
11.654133236621 |
L(r)(E,1)/r! |
Ω |
0.21948217898595 |
Real period |
R |
1.0211213862344 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999199 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81984bx1 2562b1 |
Quadratic twists by: -4 8 |