Elliptic curves in honeycomb form

Details Elliptic curves in honeycomb form Elliptic curves in honeycomb form

2012-03-11

arxiv.org/abs/1203.2356v1

Mathematics

Algebraic Geometry

20 pages, 5 figures

Scientific paper

A plane cubic curve, defined over a field with valuation, is in honeycomb form if its tropicalization exhibits the standard hexagonal cycle. We explicitly compute such representations from a given j-invariant with negative valuation, we give an analytic characterization of elliptic curves in honeycomb form, and we offer a detailed analysis of the tropical group law on such a curve.

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