Atkin-Lehner |
2- 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368ey |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
53248 |
Modular degree for the optimal curve |
Δ |
-30743691264 = -1 · 215 · 38 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- -1 1 11- 13- 8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-588,10064] |
[a1,a2,a3,a4,a6] |
Generators |
[10:-72:1] |
Generators of the group modulo torsion |
j |
-941192/1287 |
j-invariant |
L |
6.3527188871452 |
L(r)(E,1)/r! |
Ω |
1.0579466812557 |
Real period |
R |
0.75059535140575 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999988353 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368eb1 41184g1 27456bm1 |
Quadratic twists by: -4 8 -3 |