Heights of points on elliptic curves over \mathbb Q

2020/07/18 by Griffin, Michael, Ono, Ken, Tsai, Wei-Lun
#11G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2007.09514

Abstract

In this note we obtain effective lower bounds for the canonical heights of non-torsion points on E(ℚ) by making use of suitable elliptic curve ideal class pairings Ψ_E,-D: E(ℚ)× E_-D(ℚ)↦ CL(-D). In terms of the class number H(-D) and T_E(-D), a logarithmic function in D, we prove \widehath(P)gt; \frac|E_tor(ℚ)|²( H(-D)+ |E_tor(ℚ)|)²⋅ T_E(-D).

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