One detailed discussion of elliptic curves with lots of history is: https://www.maa.org/sites/default/files/pdf/upload_library/2/Rice-2013.pdf https://www.maa.o

One detailed discussion of elliptic curves with lots of history is: https://www.maa.org/sites/default/files/pdf/upload_library/2/Rice-2013.pdf https://www.maa.org/sites/default/files/pdf/upload_library/2... To answer your specific question: "Elliptic curves have almost nothing to do with ellipses at all. Why then are they called elliptic curves? The answer lies in the word almost. There is a connection between ellipses and elliptic curves, but it’s not at all obvious and is the result of a connected but distinctly nonlinear sequence of mathematical events."