On a Conjecture of Birch and Swinnerton-Dyer

By Wentang Kuo, M. Murty. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2005

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Unearthing the visions of a master: harmonic Maass forms and number theory (2008, background): “18Coates and Wiles [79] earlier proved that L(E, 1) 6= 0 =⇒ rk(E) = 0 for elliptic curves E/Q with complex multiplication.”
Congruent numbers and Heegner points (2012, background): “(2) the 2-adic additive valuation of L(E, 1) is not less than 2s−1 and the equality holds if and only if the ideal class group A of Q( √ −2m) satisfies that dimF2 A[4]/A[2] = 1 and s ∏”
Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, result): “(In the CM case, some early results were obtained by Coates-Wiles [13]).”
The main conjecture for CM elliptic curves at supersingular primes (2005, methodology): “t character χ. Let ΩE ∈ R+ denote the real period of a minimal model of E. 456 ROBERT POLLACK AND KARL RUBIN The explicit reciprocity law of Wiles [Wi] together with a computation of Coates and Wiles [CW] leads to the following theorem, which is the step labeled (b) in the introduction. Theorem 5.1.”