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On Mordell‐Weil Lattices of Type D 5
Author(s) -
Usui Hisashi
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931610116
Subject(s) - mathematics , elliptic curve , rank (graph theory) , type (biology) , pure mathematics , algebraic number , algebra over a field , mathematical analysis , combinatorics , ecology , biology
We establish the analogue for D 5 of the theory of algebraic equation of type E r (T. SHIODA: Construction of elliptic curves with high rank via the invariants of the Weyl groups, J. Math. Soc. Japan 43 , 1991, No. 4, 673‐719), which is one of the results of the theory of Mordell‐Weil lattices. As an application, we give a method of constructing an elliptic curve over Q( t ) with rank 5, together with explicit generators of the Mordell‐Weil group.