TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 10
IS - 2
PY - 2015
Y1 - 2015/10/01
TI - On the Elliptic Curves of the Form $y^2 = x^3 − pqx$
TT -
N2 - 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 infinite 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.
SP - 77
EP - 86
AU - Daghigh, H.
AU - Didari, S.
AD - University of Kashan
KW - Diophantine equation
KW - Elliptic curves
KW - Mordell weil group
KW - Selmer group
KW - Birch and Swinnerton- dyer conjecture
KW - Parity conjecture.
UR - http://ijmsi.ir/article-1-570-en.html
DO - 10.7508/ijmsi.2015.02.008
ER -