We define the notion of special automorphisms on Shimura curves. Using this notion, for a wild class of elliptic curves defined over Q, we get rank one quadratic twists by discriminants having any prescribed number of...We define the notion of special automorphisms on Shimura curves. Using this notion, for a wild class of elliptic curves defined over Q, we get rank one quadratic twists by discriminants having any prescribed number of prime factors. Finally, as an application, we obtain some new results on Birch and Swinnerton-Dyer(BSD) conjecture for the rank one quadratic twists of the elliptic curve X_0(49).展开更多
文摘We define the notion of special automorphisms on Shimura curves. Using this notion, for a wild class of elliptic curves defined over Q, we get rank one quadratic twists by discriminants having any prescribed number of prime factors. Finally, as an application, we obtain some new results on Birch and Swinnerton-Dyer(BSD) conjecture for the rank one quadratic twists of the elliptic curve X_0(49).
