Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368cb |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
163840 |
Modular degree for the optimal curve |
Δ |
231838656192 = 26 · 311 · 112 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -4 4 11- 13+ 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2487,41740] |
[a1,a2,a3,a4,a6] |
Generators |
[152:1782:1] |
Generators of the group modulo torsion |
j |
36462258496/4969107 |
j-invariant |
L |
5.3673237021132 |
L(r)(E,1)/r! |
Ω |
0.95423868607214 |
Real period |
R |
1.4061795493289 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999643 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bb1 41184bb2 27456z1 |
Quadratic twists by: -4 8 -3 |