Atkin-Lehner |
2+ 5+ 7+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
82600d |
Isogeny class |
Conductor |
82600 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-42410763500000000 = -1 · 28 · 59 · 7 · 594 |
Discriminant |
Eigenvalues |
2+ -1 5+ 7+ -1 -3 -5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-59633,11403637] |
[a1,a2,a3,a4,a6] |
Generators |
[47:2950:1] [-303:1250:1] |
Generators of the group modulo torsion |
j |
-5863149638656/10602690875 |
j-invariant |
L |
8.4609039995953 |
L(r)(E,1)/r! |
Ω |
0.32279709059584 |
Real period |
R |
0.81910047421504 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000192 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16520d1 |
Quadratic twists by: 5 |