Atkin-Lehner |
2- 5+ 13+ 79+ |
Signs for the Atkin-Lehner involutions |
Class |
82160i |
Isogeny class |
Conductor |
82160 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-17089280 = -1 · 28 · 5 · 132 · 79 |
Discriminant |
Eigenvalues |
2- -1 5+ 1 -1 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1901,32545] |
[a1,a2,a3,a4,a6] |
Generators |
[21:38:1] [24:13:1] |
Generators of the group modulo torsion |
j |
-2969330458624/66755 |
j-invariant |
L |
8.5938345468431 |
L(r)(E,1)/r! |
Ω |
2.0264152148505 |
Real period |
R |
1.060226266029 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000212 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20540a1 |
Quadratic twists by: -4 |