"Generators and number fields for torsion points of a special elliptic curve"

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Let E be an elliptic curve with Weierstrass form y2=x3−px, where p is a prime number and let E[m] be its m-torsion subgroup. Let p1=(x1,y1) and p2=(x2,y2) be a basis… Click to show full abstract

Let E be an elliptic curve with Weierstrass form y2=x3−px, where p is a prime number and let E[m] be its m-torsion subgroup. Let p1=(x1,y1) and p2=(x2,y2) be a basis for E[m], then we prove that ℚ(E[m])=ℚ(x1,x2,ξm,y1) in general. We also find all the generators and degrees of the extensions ℚ(E[m])/ℚ for m=3 and m=4.

Keywords: http www; mrow; jats inline; xlink; math; inline formula

Journal Title: Arab Journal of Mathematical Sciences
Year Published: 2019

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