Atkin-Lehner |
2+ 3- 29+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
8178g |
Isogeny class |
Conductor |
8178 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
7488 |
Modular degree for the optimal curve |
Δ |
1448708166 = 2 · 312 · 29 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 3 -4 0 -1 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1052,12908] |
[a1,a2,a3,a4,a6] |
j |
128581165173817/1448708166 |
j-invariant |
L |
2.0269373406689 |
L(r)(E,1)/r! |
Ω |
1.5202030055017 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
65424h1 24534w1 |
Quadratic twists by: -4 -3 |