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- Title
A GEOMETRIC APPROACH TO ELLIPTIC CURVES WITH TORSION GROUPS ℤ/10ℤ, ℤ/12ℤ, ℤ/14ℤ, AND ℤ/16ℤ.
- Authors
HALBEISEN, LORENZ; HUNGERBÜHLER, NORBERT; ZARGAR, ARMAN SHAMSI; VOZNYY, MAKSYM
- Abstract
We give new parametrisations of elliptic curves in Weierstrass normal form y ² = x ³ + ax² + bx with torsion groups ℤ/10ℤ and ℤ/12ℤ over Q, and with ℤ/14ℤ and ℤ/16ℤ over quadratic fields. Even though the parametrisations are equivalent to those given by Kubert and Rabarison, respectively, with the new parametrisations we find three infinite families of elliptic curves with torsion group ℤ/12ℤ and positive rank. Furthermore, we find elliptic curves with torsion group ℤ/14ℤ and rank 3 – which is a new record for such curves – as well as some new elliptic curves with torsion group ℤ/16ℤ and rank 3.
- Subjects
ELLIPTIC curves; QUADRATIC fields; POLYNOMIALS; APPROXIMATION theory; ALGEBRAIC curves
- Publication
Rad HAZU: Matematicke Znanosti, 2023, Vol 27, p87
- ISSN
1845-4100
- Publication type
Article
- DOI
10.21857/ydkx2coje9