Atkin-Lehner |
2- 3+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
83664be |
Isogeny class |
Conductor |
83664 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
25344 |
Modular degree for the optimal curve |
Δ |
-182973168 = -1 · 24 · 39 · 7 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- -6 -3 1 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,135,243] |
[a1,a2,a3,a4,a6] |
Generators |
[18:189:8] |
Generators of the group modulo torsion |
j |
864000/581 |
j-invariant |
L |
5.3238804482771 |
L(r)(E,1)/r! |
Ω |
1.1312551495008 |
Real period |
R |
2.353085616877 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000010632 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20916d1 83664bh1 |
Quadratic twists by: -4 -3 |