Atkin-Lehner |
3- 11- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
21417k |
Isogeny class |
Conductor |
21417 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
48576 |
Modular degree for the optimal curve |
Δ |
-60440844445641 = -1 · 34 · 118 · 592 |
Discriminant |
Eigenvalues |
1 3- -3 2 11- -1 -1 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,7015,298505] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:193:1] |
Generators of the group modulo torsion |
j |
178137047/281961 |
j-invariant |
L |
6.0813461347941 |
L(r)(E,1)/r! |
Ω |
0.42518907835634 |
Real period |
R |
1.7878358253882 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64251ba1 21417m1 |
Quadratic twists by: -3 -11 |