In this paper we consider elliptic curves, conics and cubic congruences over finite fields associated with indefinite binary quadratic forms $F_i$ in the proper cycle of $F=(1,7,-6)$. We determine the number of rational points on elliptic curves $E_{F_i}:y^2=a_ix^3+b_ix^2+c_ix$ and conics $C_{F_i}:a_ix^2+b_ix^y+c_iy^2-N=0$ over $\mathbb F_{73}$, where $N\in\mathbb F_{73}^*$ and $F_i=(a_i,b_i,c_i)$ be any form in the proper cycle of $F$. In the last section, we consider the number integer solutions of cubic congruences $C_{F_i}:x^3+a_ix^2+b_ix+C_i=0(\mod73)$ associated with $F_i$.