PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Primitive divisors of elliptic divisibility sequences for elliptic curves with $j=1728$

Volume 198 / 2021

Matteo Verzobio Acta Arithmetica 198 (2021), 129-168 MSC: Primary 11G05, 11B39; Secondary 11A41, 11D59, 11G07, 11G50. DOI: 10.4064/aa191016-30-7 Published online: 4 January 2021


Take a rational elliptic curve defined by the equation $y^2=x^3+ax$ in minimal form and consider the sequence $B_n$ of the denominators of the abscissas of the iterate of a non-torsion point. We show that $B_{5m}$ has a primitive divisor for every $m$. Then, we show how to generalize this method to the terms of the form $B_{mp}$ with $p$ a prime congruent to $1$ modulo $4$.


  • Matteo VerzobioDepartment of Mathematics
    Università di Pisa
    Largo Bruno Pontecorvo 5
    Pisa, Italy

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image