Atkin-Lehner |
3+ 5+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
83205b |
Isogeny class |
Conductor |
83205 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
20160 |
Modular degree for the optimal curve |
Δ |
181969335 = 39 · 5 · 432 |
Discriminant |
Eigenvalues |
-1 3+ 5+ -1 1 2 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-218,-998] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:17:1] [20:38:1] |
Generators of the group modulo torsion |
j |
31347/5 |
j-invariant |
L |
6.5608085711655 |
L(r)(E,1)/r! |
Ω |
1.2563053180913 |
Real period |
R |
2.611152112802 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997693 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
83205f1 83205e1 |
Quadratic twists by: -3 -43 |