Group generated by total sextactic points of a family of quartic curves

Abstract

The aim of this paper is to study the group generated by the total sextactic points in the Jacobian of the family of smooth quartic curves given by the equation: $$C_a:Y^4=XZ\left(X-Z\right)\left(X-aZ\right),a\in \mathbb{C}\backslash \{0,1\}.$$

Keywords:

• Algebraic curves
• elliptic curves
• flex points
• Jacobian
• quartic curves
• sextactic points

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 11G30
• Secondary: 14H45

Acknowledgments

Alwaleed Kamel would like to express his thanks and gratitude to Dr. Masumi KAWASAKI (Kaijo Junior & Senior High school, Shinjuku-ku, Tokyo, Japan) for everything he learned from him during his stay at Saitama University, Japan.

Additional information

Funding

Mohammed A. Saleem and Waleed K. Elshareef were funded by the Academy of Scientific Research and Technology, Egypt, under ScienceUP Grant No. 6492.