Atkin-Lehner |
2- 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368ei |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
65536 |
Modular degree for the optimal curve |
Δ |
-138346610688 = -1 · 214 · 310 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 0 11+ 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1284,-2576] |
[a1,a2,a3,a4,a6] |
Generators |
[5:63:1] [29:243:1] |
Generators of the group modulo torsion |
j |
19600688/11583 |
j-invariant |
L |
10.084257616319 |
L(r)(E,1)/r! |
Ω |
0.60676569968376 |
Real period |
R |
4.1549224114221 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999263 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368ck1 20592i1 27456cm1 |
Quadratic twists by: -4 8 -3 |