Year 2020, Volume 49 , Issue 4, Pages 1458 - 1470 2020-08-06

Sequences associated to elliptic curves with non-cyclic torsion subgroup

Betül GEZER [1]


Let $E$ be an elliptic curve defined over $K$ given by a Weierstrass equation and let $P=(x,y)\in E(K)$ be a point. Then for each $n$ $\geq 1$ we can write the $x$- and $y$-coordinates of the point $[n]P$ as
\[ [n]P=\left( \frac{G_{n}(P)}{F_{n}^{2}(P)},\frac{H_{n}(P)}{F_{n}^{3}(P)}\right)\]
where $F_{n}$, $G_{n}$, and $H_{n}\in K[x,y]$ are division polynomials of $E$. In this work we give explicit formulas for sequences
\[(F_{n}(P))_{n\geq 0},\,(G_{n}(P))_{n\geq 0},\,\text{and}\,(H_{n}(P))_{n\geq 0}\]
associated to an elliptic curve $E$ defined over $\mathbb{Q}$ with non-cyclic torsion subgroup. As applications we give similar formulas for elliptic divisibility sequences associated to elliptic curves with non-cyclic torsion subgroup and determine square terms in these sequences.
Elliptic curves, division polynomials, elliptic divisibility sequences
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-9133-1734
Author: Betül GEZER (Primary Author)
Institution: BURSA ULUDAĞ ÜNİVERSİTESİ
Country: Turkey


Dates

Publication Date : August 6, 2020

Bibtex @research article { hujms464130, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1458 - 1470}, doi = {10.15672/hujms.464130}, title = {Sequences associated to elliptic curves with non-cyclic torsion subgroup}, key = {cite}, author = {Gezer, Betül} }
APA Gezer, B . (2020). Sequences associated to elliptic curves with non-cyclic torsion subgroup . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1458-1470 . DOI: 10.15672/hujms.464130
MLA Gezer, B . "Sequences associated to elliptic curves with non-cyclic torsion subgroup" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1458-1470 <https://dergipark.org.tr/en/pub/hujms/issue/56305/464130>
Chicago Gezer, B . "Sequences associated to elliptic curves with non-cyclic torsion subgroup". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1458-1470
RIS TY - JOUR T1 - Sequences associated to elliptic curves with non-cyclic torsion subgroup AU - Betül Gezer Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.464130 DO - 10.15672/hujms.464130 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1458 EP - 1470 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.464130 UR - https://doi.org/10.15672/hujms.464130 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Sequences associated to elliptic curves with non-cyclic torsion subgroup %A Betül Gezer %T Sequences associated to elliptic curves with non-cyclic torsion subgroup %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.464130 %U 10.15672/hujms.464130
ISNAD Gezer, Betül . "Sequences associated to elliptic curves with non-cyclic torsion subgroup". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1458-1470 . https://doi.org/10.15672/hujms.464130
AMA Gezer B . Sequences associated to elliptic curves with non-cyclic torsion subgroup. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1458-1470.
Vancouver Gezer B . Sequences associated to elliptic curves with non-cyclic torsion subgroup. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1458-1470.