On the vertices of the elliptic curves (Q2834845)
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scientific article; zbMATH DE number 6655803
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the vertices of the elliptic curves |
scientific article; zbMATH DE number 6655803 |
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24 November 2016
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metric classification of elliptic curves
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metric classification of algebraic curves
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vertices
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curvature function
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On the vertices of the elliptic curves (English)
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The aim of this paper is to investigate the elliptic curves, expressed in the Weierstrass form, using techniques of classical differential geometry. The authors show that these elliptic curves are completely determined by a point and the velocity vector at that point, behaving like geodesics. They investigate the number of their vertices. The curvature function is carefully studied and bounds for the number of vertices of the elliptic curves are given. As a generalization, a program for the classification of algebraic curves is sketched, using geometric invariants. For conics (and partially for cubics), the authors give the tables with the respective classes.
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0.7255199551582336
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0.7092966437339783
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