Displaying similar documents to “On Tate-Shafarevich groups of y 2 = x ( x 2 - k 2 ) .”

3-Selmer groups for curves y 2 = x 3 + a

Andrea Bandini (2008)

Czechoslovak Mathematical Journal

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We explicitly perform some steps of a 3-descent algorithm for the curves y 2 = x 3 + a , a a nonzero integer. In general this will enable us to bound the order of the 3-Selmer group of such curves.

Why is the class number of ℚ ( 11 3 ) even?

F. Lemmermeyer (2013)

Mathematica Bohemica

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In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.

Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.

Carlos Munuera Gómez (1991)

Extracta Mathematicae

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Let p be a prime number, p ≠ 2,3 and Fp the finite field with p elements. An elliptic curve E over Fp is a projective nonsingular curve of genus 1 defined over Fp. Each one of these curves has an isomorphic model given by an (Weierstrass) equation E: y2 = x3 + Ax + B, A,B ∈ Fp with D = 4A3 + 27B2 ≠ 0. The j-invariant of E is defined...