Atkin-Lehner |
3+ 7- 13+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
82173b |
Isogeny class |
Conductor |
82173 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
103680 |
Modular degree for the optimal curve |
Δ |
-609056990451 = -1 · 33 · 79 · 13 · 43 |
Discriminant |
Eigenvalues |
0 3+ -3 7- -3 13+ 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,1013,-35778] |
[a1,a2,a3,a4,a6] |
Generators |
[54:416:1] |
Generators of the group modulo torsion |
j |
976191488/5176899 |
j-invariant |
L |
2.2203016394483 |
L(r)(E,1)/r! |
Ω |
0.45962338791076 |
Real period |
R |
2.4153488447051 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006616 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11739i1 |
Quadratic twists by: -7 |