Stankewicz, Torsion points on elliptic curves with complex multi- plication (with an appendix by Alex Rice). International Journal of Number Theory 9 (2013), 447-479.P.L. Clark; B. Cook; J. Stankewicz, Torsion points on elliptic curves with complex multiplica- tion, International Journal ...
We prove that there are only finitely many complex numbers $a$ and $b$ with $4a^3+27b^2\not=0$ such that the three points $(1,*),(2,*),$ and $(3,*)$ are simultaneously torsion on the elliptic curve defined in Weierstrass form by $y^2=x^3+ax+b$. This give
Most Elliptic Curves over Global Function Fields are Torsion Free Given an elliptic curve E E over a global function field K K , the Galois action on the n n -torsion points of E E gives rise to a mod-n Galois representation ho_{E,n} ho_{E,n} . For K K satisfying some mild co...
Torsion points on elliptic curves We announce a proof (in the quadratic case) of the classical conjecture that if E is an elliptic curve possessing a rational torsion point of order N defin... S Kamienny - 《Bulletin of the American Mathematical Society》 被引量: 261发表: 1990年 TORSION ...
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TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE) We present seven theorems on the structure of prime order torsion points on CM elliptic curves defined over number fields. The first three results refine b... PL Clark,B Cook,J Stankewicz - 《Intern...
Torsion points on elliptic curves over number fields of small degree We determine the set $S(d)$ of possible prime orders of $K$-rational points on elliptic curves over number fields $K$ of degree $d$, for $d = 4,5$ and $6$. M Derickx,S Kamienny,W Stein,... 被引量: 0发表:...
Some remarks on torsion in elliptic curves - Kamienny - 1995 () Citation Context ...e classified all the cases and hence reduced Euler’s problem to a question of ranks. In [6], Parshin obtaines an inequality to give an effective bound for the height of rational points on a curve. In...
Torsion Points on Elliptic Curves in Weierstrass Form We prove that there are only finitely many complex numbers $a$ and $b$ with $4a^3+27b^2\not=0$ such that the three points $(1,*),(2,*),$ and $(3,*)$ are si... P Habegger - 《Annali Della Scuola Normale Superiore Di Pis...
Computing Torsion Points on Curves, Experiment - Poonen () Citation Context ...t of Q ′ 2 can be specified exactly with a finite amount of data. On the other hand, Q ′ 2 approximates Q2 well in the sense that C(Q ′ 2) is dense in C(Q2) and J(Q ′ 2) is dense in J(...