Atkin-Lehner |
2+ 3+ 19- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
81168k |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
-140258304 = -1 · 210 · 34 · 19 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -4 -1 -1 1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,24,-576] |
[a1,a2,a3,a4,a6] |
Generators |
[8:8:1] [12:36:1] |
Generators of the group modulo torsion |
j |
1431644/136971 |
j-invariant |
L |
7.5837226388981 |
L(r)(E,1)/r! |
Ω |
0.87333473387212 |
Real period |
R |
1.0854547438749 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998946 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40584v1 |
Quadratic twists by: -4 |