On the Rank of Elliptic Curves in Elementary Cubic Extensions
Keyword(s):
We give a method for explicitly constructing an elementary cubic extension L over which an elliptic curve ED:y2+Dy=x3 (D∈Q∗) has Mordell-Weil rank of at least a given positive integer by finding a close connection between a 3-isogeny of ED and a generic polynomial for cyclic cubic extensions. In our method, the extension degree [L:Q] often becomes small.
2005 ◽
Vol 48
(1)
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pp. 16-31
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2012 ◽
Vol 149
(2)
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pp. 175-203
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2002 ◽
Vol 5
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pp. 127-174
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2015 ◽
Vol 18
(1)
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pp. 578-602
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2016 ◽
Vol 13
(01)
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pp. 133-152
2011 ◽
Vol 07
(03)
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pp. 739-769
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2001 ◽
Vol 131
(3)
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pp. 385-404
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