Elliptic curves and rational distance sets
نویسندگان
چکیده
منابع مشابه
Towers of Curves and Rational Distance Sets
A rational (resp. integral) distance set is a subset S of the plane R such that for all s, t ∈ S, the distance between s and t is a rational number (resp. is an integer). Huff [4] considered rational distance sets S of the following form: given distinct a, b ∈ Q∗, S contains the four points (0,±a) and (0,±b) on the y-axis, plus points (x, 0) on the x-axis, for some x ∈ Q∗. Such a point (x, 0) m...
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Let A be an elliptic curve over Q of square free conductor N . Suppose A has a rational torsion point of prime order r such that r does not divide 6N . We prove that then r divides the order of the cuspidal subgroup C of J0(N). If A is optimal, then viewing A as an abelian subvariety of J0(N), our proof shows more precisely that r divides the order of A ∩ C. Also, under the hypotheses above, we...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1954
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1954-0060262-1