K. Rubin, Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 64 (1981), 455-470.  Home/Search   Document Details and Download   Summary   Related Articles

....1 is equal to r. The conjecture further says that the leading coefficient in the Taylor expansion at s = 1 can be expressed in terms of certain number theoretic invariants of E. Starting in 1977, a series of important partial results have been proved in support of this fundamental conjecture (see [5, 6, 25]) but in its most general form it remains a very difficult unsolved problem. 2.4 Heights Let E be an elliptic curve (in Weierstrass form) over the field Q of rational numbers. Let P = x; y) be a rational point on E (not the point at infinity) The logarithmic height of P is defined by the ....

K. Rubin, Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 64 (1981), 455-470.

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