Atkin-Lehner |
2+ 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368cc |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-988476710756401152 = -1 · 214 · 320 · 113 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 11- 13- 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,102660,46128656] |
[a1,a2,a3,a4,a6] |
j |
10017976862000/82759712607 |
j-invariant |
L |
2.4378339752594 |
L(r)(E,1)/r! |
Ω |
0.20315283133975 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368dy1 10296i1 27456f1 |
Quadratic twists by: -4 8 -3 |