Straight-line programs and torsion points on elliptic curves
نویسندگان
چکیده
منابع مشابه
Torsion Points of Elliptic Curves
Elliptic curves as an area of mathematical study are initially simple to understand, but reveal startling complexity when considered over different fields. This paper discusses the general properties and characteristics of projective space, elliptic curves, and the group structure that arises with certain binary operations on the curve. We discuss elliptic curves over Q, including the topic of ...
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Let k be an algebraically closed field, char k 6= 2, 3, and let X ⊂ P be an elliptic curve with defining polynomial f . We show that any non-trivial torsion point of order r, determines up to equivalence, a unique minimal matrix Φr of size 3r×3r with linear polynomial entries such that det Φr = f . We also show that the identity, thought of as the trivial torsion point of order r, determines up...
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Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, ρE : Gal(k/k) → GL2(b Z). For a fixed number field k, we describe the image of ρE for a “random” elliptic curve E over k. In particular, if k 6= Q is linearly disjoint from the cyclotomic extension of Q, then ρE will be surjective for “most” elliptic curves over k.
متن کاملAlmost Rational Torsion Points on Semistable Elliptic Curves
If P is an algebraic point on a commutative group scheme A/K, then P is almost rational if no two non-trivial Galois conjugates σP , τP of P have sum equal to 2P . In this paper, we classify almost rational torsion points on semistable elliptic curves over Q. 1 Definitions and Results Let X be an algebraic curve of genus greater than one. Let J(X) be the Jacobian variety of X, and embed X in J(...
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ژورنال
عنوان ژورنال: computational complexity
سال: 2003
ISSN: 1016-3328,1420-8954
DOI: 10.1007/s00037-003-0180-0