most recent 30 from http://mathoverflow.net 2013-05-22T12:31:59Z http://mathoverflow.net/feeds/question/97851 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/97851/uniform-bounds-for-the-order-of-a-rational-torsion-point-on-cm-elliptic-curves Adam Harris 2012-05-24T16:44:01Z 2012-08-24T18:58:45Z

<p>Let $K$ be an imaginary quadratic field and $E$ an elliptic curve with CM by the maximal order of $K$, such that $E$ is defined over the Hilbert class field $H$. Is it known whether there is a bound (independent of the degree of $H$) on the order of a $H$-rational torsion point on $E$?</p>

http://mathoverflow.net/questions/97851/uniform-bounds-for-the-order-of-a-rational-torsion-point-on-cm-elliptic-curves/105411#105411 stankewicz 2012-08-24T18:58:45Z 2012-08-24T18:58:45Z

<p>Hey, I probably should have answered this one some time ago. It was proved in 1989 by J.L. Parish that the order of an $H$-rational torsion point is 1,2,3,4 or 6, and this also can be deduced from work of either Silverberg or Prasad-Yogananda. In any case the statement you want is at the beginning of section VI in the paper below and the proof is done in section V.</p> <p><a href="http://www.sciencedirect.com/science/article/pii/0022314X89900127" rel="nofollow">http://www.sciencedirect.com/science/article/pii/0022314X89900127</a></p>