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Families of Mordell Curves with Non-trivial Torsion and Rank of at Least Three

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Mathematics and Computing (ICMC 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 415))

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Abstract

In this study, we consider a particular type of elliptic curves called Mordell curves, and construct two infinite families of such curves with rank of at least three. We do this by using parametrizations due to Euler to obtain two rational points on these curves and obtain the third point from an elliptic curve of rank equal to two. We then show that the three points are of infinite order and are generally linearly independent.

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Authors and Affiliations

  1. University of the Philippines Baguio, Baguio City, 2600, Philippines

    Renz Jimwel S. Mina & Jerico B. Bacani

Authors
  1. Renz Jimwel S. Mina
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  2. Jerico B. Bacani
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Corresponding author

Correspondence to Renz Jimwel S. Mina .

Editor information

Editors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    B. Rushi Kumar

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India

    S. Ponnusamy

  3. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India

    Debasis Giri

  4. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA

    Bhavani Thuraisingham

  5. Department of Computer Science, Purdue University, West Lafayette, IN, USA

    Christopher W. Clifton

  6. Department of Theoretical and Applied Sciences, University of Insubria, Varese, Italy

    Barbara Carminati

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Mina, R.J.S., Bacani, J.B. (2022). Families of Mordell Curves with Non-trivial Torsion and Rank of at Least Three. In: Rushi Kumar, B., Ponnusamy, S., Giri, D., Thuraisingham, B., Clifton, C.W., Carminati, B. (eds) Mathematics and Computing. ICMC 2022. Springer Proceedings in Mathematics & Statistics, vol 415. Springer, Singapore. https://doi.org/10.1007/978-981-19-9307-7_13

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