Atkin-Lehner |
2+ 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368j |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
3953664 = 210 · 33 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 11- 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-576,5320] |
[a1,a2,a3,a4,a6] |
Generators |
[17:21:1] [41:225:1] |
Generators of the group modulo torsion |
j |
764411904/143 |
j-invariant |
L |
9.8190097476373 |
L(r)(E,1)/r! |
Ω |
2.4027918767958 |
Real period |
R |
4.0865003092804 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999744 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368cr1 5148a1 82368b1 |
Quadratic twists by: -4 8 -3 |