Atkin-Lehner |
2- 3+ 7+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
82992bf |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-15685488 = -1 · 24 · 34 · 72 · 13 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ 2 13+ -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,62,19] |
[a1,a2,a3,a4,a6] |
Generators |
[1:9:1] [9:35:1] |
Generators of the group modulo torsion |
j |
1620896000/980343 |
j-invariant |
L |
9.385531994097 |
L(r)(E,1)/r! |
Ω |
1.3557016650104 |
Real period |
R |
1.7307517273955 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998914 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20748p1 |
Quadratic twists by: -4 |