令E 為定義在有理數上的一條橢圓曲線。假設E 有二次體中整數環的複乘數而且E 在質數q 為超奇異化歸。令P 為橢圓曲線E 上的有理點而且其階為無窮。令L 是K 加進所有q-扭轉點及所有Q 滿足[q]Q=P 的座標的擴張體。本計畫希望深入探討這個伽羅瓦擴張。 Let E be an elliptic curve defined over the rational numbers. Suppose that E has complex multiplication by a maximal order of an imaginary quadratic field K and has good supersingular reduction at a prime q. Let P be a rational point on E of infinite order. Denote by L the extension field joining the coordinates of q-torsion points of E and also the coordinates of all points Q satisfying [q]Q=P. In this project, we study the Galois extension L over K. 研究期間：9908 ~ 10007
