Atkin-Lehner |
2+ 3+ 7- 101+ |
Signs for the Atkin-Lehner involutions |
Class |
89082g |
Isogeny class |
Conductor |
89082 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
53760 |
Modular degree for the optimal curve |
Δ |
-431869536 = -1 · 25 · 33 · 72 · 1012 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- 1 4 -8 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-261,1973] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:64:1] [46:179:8] |
Generators of the group modulo torsion |
j |
-1489433211/326432 |
j-invariant |
L |
7.3146898801838 |
L(r)(E,1)/r! |
Ω |
1.6010378810016 |
Real period |
R |
1.1421793897441 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000091 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89082bc1 89082a1 |
Quadratic twists by: -3 -7 |