Atkin-Lehner |
2+ 3+ 5+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
63840b |
Isogeny class |
Conductor |
63840 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
20632449600 = 26 · 36 · 52 · 72 · 192 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ -4 2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5986,180136] |
[a1,a2,a3,a4,a6] |
Generators |
[-82:336:1] [6:380:1] |
Generators of the group modulo torsion |
j |
370703277125056/322382025 |
j-invariant |
L |
7.8703304514891 |
L(r)(E,1)/r! |
Ω |
1.2055001908393 |
Real period |
R |
3.2643422669271 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
63840bu1 127680ct2 |
Quadratic twists by: -4 8 |