  The class number divisibility problem for number fields is one of the
classical problems in algebraic number theory, which originated from Gauss'
class number conjectures. The relation between the points on an elliptic curve
and class number divisibility of a number field has been explored through the
works of various mathematicians. Here, we explicitly construct an unramified
abelian extension of a bi-quadratic field generated from points of a certain
type of elliptic curve. Moreover, showing the $2$-Selmer rank of the said
elliptic curve as $1$, we also construct an infinite family of bi-quadratic
fields of even class number.
