Atkin-Lehner |
3- 5+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
86775q |
Isogeny class |
Conductor |
86775 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1651200 |
Modular degree for the optimal curve |
Δ |
-47137298583984375 = -1 · 3 · 516 · 13 · 892 |
Discriminant |
Eigenvalues |
-1 3- 5+ -4 4 13+ 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-2317688,1357943367] |
[a1,a2,a3,a4,a6] |
Generators |
[114069:6930578:27] |
Generators of the group modulo torsion |
j |
-88118808127805290681/3016787109375 |
j-invariant |
L |
4.4240238667132 |
L(r)(E,1)/r! |
Ω |
0.33475854804293 |
Real period |
R |
6.6077832856202 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999768538 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17355g1 |
Quadratic twists by: 5 |