Atkin-Lehner |
3+ 5+ 17+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
21165b |
Isogeny class |
Conductor |
21165 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
663264 |
Modular degree for the optimal curve |
Δ |
1939715788063359375 = 36 · 57 · 177 · 83 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 0 -3 1 17+ 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-5171936,-4528839742] |
[a1,a2,a3,a4,a6] |
Generators |
[-51320178:45799447:39304] |
Generators of the group modulo torsion |
j |
15299708047799453412761089/1939715788063359375 |
j-invariant |
L |
2.2222267141115 |
L(r)(E,1)/r! |
Ω |
0.10011279182169 |
Real period |
R |
11.098615240245 |
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 |
63495l1 105825e1 |
Quadratic twists by: -3 5 |