Abstract: We determine the ranks of elliptic curves and denoted, respectively, by , and with prime p. We compute the ranks of and which are elliptic curves and with prime p and compare the results with those of previous curves. In addition, we find ranks of and and compare the results with those of and |
Keywords and phrases: prime, elliptic curves.
Received: March 11, 2021; Accepted: April 27, 2021; Published: July 3, 2021
How to cite this article: Shin-Wook Kim, Ranks of some elliptic curves , JP Journal of Algebra, Number Theory and Applications 51(2) (2021), 223-248. DOI: 10.17654/NT051020223
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] C. Caldwell, http://primes.utm.edu/curios/includes/primetest.php. [2] S. W. Kim, Considering in rank of Far East J. Math. Sci. (FJMS) 96(7) (2015), 899-911. [3] S. W. Kim, Ranks of elliptic curves Int. J. Algebra 9(5) (2015), 205-211. http://dx.doi.org/10.12988/ija.2015.5421. [4] S. W. Kim, Crucial function of prime’s form, Int. J. Algebra 10(6) (2016), 283-290. http://dx.doi.org/10.12988/ija.2016.6428. [5] S. W. Kim, Comparison of ranks in some elliptic curves, JP J. Algebra, Number Theory and Applications 40(5) (2018), 725-743. [6] S. W. Kim, Various forms in components of primes, Int. J. Algebra 13(2) (2019), 59-72. https://doi.org/10.12988/ija.2019.913. [7] S. W. Kim, Algebraic structure in elliptic curves Int. J. Algebra 13(3) (2019), 143-152. https://doi.org/10.12988/ija.2019.9212. [8] S. W. Kim, Enumeration in ranks of various elliptic curves Int. J. Algebra 14(3) (2020), 139-162. https://doi.org/10.12988/ija.2020.91250. [9] J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer, New York, 1992. http://dx.doi.org/10.1007/978-1-4757-4252-7. [10] N. Zamani and A. Shams, On the group of the elliptic curve Euro. J. Pure Appl. Math. 8 (2015), 126-134.
|