ON THE ELLIPTIC CURVES OF THE FORM Y2 = X3-PQX

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DAGHIGH HASSAN; DIDARI SOMAYEH

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2015 | Volume:10 | Issue:2 Page(s): 77-86

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Title

ON THE ELLIPTIC CURVES OF THE FORM Y2 = X3-PQX

Author(s)

DAGHIGH HASSAN | DIDARI SOMAYEH | Issue Writer Certificate

Keywords

DIOPHANTINE EQUATION

ELLIPTIC CURVES

MORDELL WEIL GROUP

SELMER GROUP

BIRCH AND SWINNERTON- DYER CONJECTURE

PARITY CONJECTURE

Abstract

By the Mordell-Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. This paper studies the rank of the family Epq:y2=x3- pqx of ELLIPTIC CURVES, where p and q are distinct primes. We give in finite families of ELLIPTIC CURVES of the form y2=x3-pqx with rank two, three and four, assuming a conjecture of Schinzel and Sierpinski is true.

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APA: Copy

DAGHIGH, HASSAN, & DIDARI, SOMAYEH. (2015). ON THE ELLIPTIC CURVES OF THE FORM Y² = X³-PQX. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 10(2), 77-86. SID. https://sid.ir/paper/310401/en

Vancouver: Copy

DAGHIGH HASSAN, DIDARI SOMAYEH. ON THE ELLIPTIC CURVES OF THE FORM Y² = X³-PQX. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2015;10(2):77-86. Available from: https://sid.ir/paper/310401/en

IEEE: Copy

HASSAN DAGHIGH, and SOMAYEH DIDARI, “ON THE ELLIPTIC CURVES OF THE FORM Y² = X³-PQX,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 10, no. 2, pp. 77–86, 2015, [Online]. Available: https://sid.ir/paper/310401/en

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