hyperelliptic curve

Question

Please help me to solve this question:

Let $H$ be a hyperelliptic curve over $\mathbb{F}_{103}$ given by the equation $ y^2 = x^5+1$. let $J$ be the jacobian of $H$ defined over $\mathbb{F}_{103}$. Show that # H($\mathbb{F}_{103^2}$) = # J($\mathbb{F}_{103}$).

Answer 1

Magma says that $\# H(\mathbb{F}_{103})=104$ and $\# J(\mathbb{F}_{103})=10610$.

Here is the code I used:

P<x> := PolynomialRing(GF(103));
C := HyperellipticCurve(x^5+1);
#C;
J:=Jacobian(C);
#J;