Atkin-Lehner |
3- 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
8085p |
Isogeny class |
Conductor |
8085 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
1494730545 = 3 · 5 · 77 · 112 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7- 11- 2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-12986,-570669] |
[a1,a2,a3,a4,a6] |
j |
2058561081361/12705 |
j-invariant |
L |
1.7889190259759 |
L(r)(E,1)/r! |
Ω |
0.44722975649398 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
129360du1 24255bm1 40425w1 1155e1 |
Quadratic twists by: -4 -3 5 -7 |