Rank of K2 of elliptic curves

• Published in: Science in China. Series A, Mathematics, physics, astronomy Vol. 52; no. 10; pp. 2107 - 2120
• Main Authors: Ji, QingZhong, Qin, HouRong
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Science in China Press 01.10.2009
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; Néron model; elliptic curve; regulator map; 11G05; 11G55

We prove that (i) rank( K 2 ( E )) ⩾ 1 for all elliptic curves E defined over ℚ with a rational torsion point of exact order N ⩾ 4; (ii) rank( K 2 ( E )) ⩾ 1 for all but at most one ℝ-isomorphism class of elliptic curves E defined over ℚ with a rational torsion point of exact order 3. We give some s...