Mathematics — Number Theory · elliptic-form-topograph
Problem
(a) Show the quadratic form Q(x,y)=92x2−74xy+15y2 is elliptic by computing its discriminant.
(b) Find the source vertex or edge in the topograph of this form.
(c) Using the topograph of this form, find all the integer solutions of 92x2−74xy+15y2=60, and explain why your list of solutions is a complete list. (There are exactly four pairs of solutions ±(x,y), three of which will be visible in the topograph.)