On characteristic polynomials for some genus 2 and 3 curves with p-rank 1 | Applied Discrete Mathematics. Supplement. 2019. № 12. DOI: 10.17223/2226308X/12/5

On characteristic polynomials for some genus 2 and 3 curves with p-rank 1

In the paper, we study characteristic polynomials for some families of p-rank 1 genus 2 and 3 hyperelliptic curves over finite field. p-Rank is an important invariant of the curves. It imposes restrictions on the coefficients of the characteristic polynomials and, therefore, on the order of the Jacobian. In this work, we distinguish several classes of p-rank 1 curves among curves with authomorphims and find characteristic polynomials for these curves modulo p.

Download file

Counter downloads: 155

Keywords

гиперэллиптические кривые, р-ранг, характеристические многочлены, группа автоморфизмов, hyperelliptic curves, p-rank, characteristic polynomial, authomorphism group

Authors

Name	Organization	E-mail
Melnichuk E.M.	I. Kant Baltic Federal University	emelnichuk39@gmail.com
Novoselov S.A.	I. Kant Baltic Federal University	snovoselov@kantiana.ru

Всего: 2

References

Singh V., ZatysevA., and McGuire G. On the Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties of Dimension up to 7 over Finite Fields. arXiv preprint arXiv:1011.2257. 2010.

Novoselov S. A. Hyperelliptic curves, Cartier - Manin matrices and Legendre polynomials // Прикладная дискретная математика. 2017. №37. С. 20-31.

Мельничук Е. М., Новоселов С. А. p-Ранги гиперэллиптических кривых рода 3 с нетривиальной группой автоморфизмов // Труды математического центра имени Н. И. Лобачевского. 2018. Т. 56. C. 188-192.

Bouw I.I., Diem C., and Scholten J. Ordinary elliptic curves of high rank over with constant j-invariant // Manuscripta Mathematica. 2004. V. 114. No. 4. P. 487-501.

Novoselov S. A. Counting points on hyperelliptic curves of type y2 = x29+1 + ax9+1 + bx. https://arxiv.org/abs/1902.05992. 2019.