One of my favourite and most studied algebraic curve is the elliptic curve. But something that I have never asked myself is: Why do they call this nonsingular cubic curve an "elliptic" curve? Obviously this is a question of etymology. But maybe there is some mathematical meaning to the word that I have missed in all these years reading about it.
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There is a connection with elliptic integrals see here http://www.voltage.com/blog/math-2/why-theyre-called-elliptic-curves/ – Nicky Hekster Jul 01 '14 at 10:05
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3Voltage link is dead – Catskul May 04 '19 at 06:03
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Sorry.. I should have searched. Actually I had this feeling already. It should be related to the arc length of an ellipse (where the word "elliptic" integral came from). So it all started when we wanted to study elliptic integral and the first elliptic curves we knew where the elliptic curves over the complex numbers. In fact these slides answers my question:
http://www.math.rochester.edu/people/faculty/doug/mypapers/wayne1.pdf
Jose
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Also see: https://www.unf.edu/~ddreibel/mas4932/elliptic-integrals.pdf – user541686 Dec 22 '21 at 01:28