hyperelliptic curve.sagews

import matplotlib.pyplot as plt
plt.rc('text', usetex=True)
plt.rc('font',**{'family':'serif','serif':['Computer Modern Roman'],'size':14})

R.<x> = ZZ[]
f = x^5 + 1
C = HyperellipticCurve(f)
pts = [
    P for P in cartesian_product([[-20..20]]*2)
    if C.ambient_space()(list(P)+[1]) in C
]
print pts

[(-1, 0), (0, -1), (0, 1)]

g = C.plot() + points(pts,size=50,color="red")
g.show(xmin=-1.5,xmax=1.5,ymin=-2,ymax=2,title="$y^2 = x^5 + 1$",aspect_ratio=1.5)