Space Elliptic Curves
In Chapter 3, we found a group structure on the plane cubic C(M, N) by a geometric construction (the cord-and-tangent method), which depends on properties peculiar to plane cubics. Since the space curve E(M, N), the solution space of equations of the Fibonacci-Fermat type, is biregularly equivalent to C(M, N), it carries a group structure, too. It certainly is nice to recognize a group structure on the set of solutions of a system of Diophantine equations. However, we soon find that it is extremely impractical to try to copy the group structure of C(M, N) on E(M, N) via the biregular equivalence.
KeywordsGroup Structure Elliptic Curf Elliptic Function Theta Function Abelian Variety
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