Atkin-Lehner |
2- 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368df |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-45602889007104 = -1 · 230 · 33 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 2 2 11- 13- 4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,2196,-322480] |
[a1,a2,a3,a4,a6] |
j |
165469149/6443008 |
j-invariant |
L |
4.9109962122209 |
L(r)(E,1)/r! |
Ω |
0.30693726296787 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368c1 20592p1 82368cv1 |
Quadratic twists by: -4 8 -3 |