Year: 2025
Type: article
Abstract: Let E λ E_{\lambda} be the Legendre family of elliptic curves with equation Y 2 = X ( X − 1 ) ( X − λ ) Y^{2}=X(X-1)(X-\lambda) . Given a curve 𝒞, satisfying a condition on the degrees of some of its coordinates and parametrizing 𝑚 points P 1 , … , P m ∈ E λ P_{1},\ldots,P_{m}\in E_{\lambda} and 𝑛 points Q 1 , … , Q n ∈ E μ Q_{1},\ldots,Q_{n}\in E_{\mu} and assuming that those points are generically linearly independent over the generic endomorphism ring, we prove that there are at most finitely many points c 0 \mathbf{c}_{0} on 𝒞 such that there exists an isogeny ϕ : E μ ( c 0 ) → E λ ( c 0 ) \phi\colon E_{\mu(\mathbf{c}_{0})}\rightarrow E_{\lambda(\mathbf{c}_{0})} and the m + n m+n points P
Source: Forum Mathematicum
Author: Luca Ferrigno
Institution: Roma Tre University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5245466801, G7837994097
OpenAlex ID: W4415427394