Atkin-Lehner |
2+ 3+ 7+ 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
82992a |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
221952 |
Modular degree for the optimal curve |
Δ |
-57160535507712 = -1 · 28 · 317 · 7 · 13 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 3 13- -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,7223,-278987] |
[a1,a2,a3,a4,a6] |
Generators |
[23830711956:227625018289:440711081] |
Generators of the group modulo torsion |
j |
162770787034112/223283341827 |
j-invariant |
L |
6.0189459564939 |
L(r)(E,1)/r! |
Ω |
0.33358066128998 |
Real period |
R |
18.043449920344 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000188 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41496bc1 |
Quadratic twists by: -4 |