Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bp |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-22203777024 = -1 · 214 · 36 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -1 -2 11- 13+ 0 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8688,-311776] |
[a1,a2,a3,a4,a6] |
Generators |
[1622719:11554517:12167] |
Generators of the group modulo torsion |
j |
-6072054784/1859 |
j-invariant |
L |
5.0540459639997 |
L(r)(E,1)/r! |
Ω |
0.24724734103283 |
Real period |
R |
10.220627536405 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.999999999975 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368dn1 10296l1 9152b1 |
Quadratic twists by: -4 8 -3 |