Atkin-Lehner |
2+ 3- 5+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
84960j |
Isogeny class |
Conductor |
84960 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
9290376000000000 = 212 · 39 · 59 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 3 -1 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-55128,-1820752] |
[a1,a2,a3,a4,a6] |
Generators |
[-172:1604:1] |
Generators of the group modulo torsion |
j |
6205159461376/3111328125 |
j-invariant |
L |
6.018575939397 |
L(r)(E,1)/r! |
Ω |
0.32829692372058 |
Real period |
R |
4.5831802741959 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998264 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84960h1 28320s1 |
Quadratic twists by: -4 -3 |