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Jan 10, 2013 at 14:43 comment added Dave M da C Hi Tim. I have had a look at that paper and there don't seem to be any precise conjectures, however it may be possible to adapt some of his arguements to find some lower bounds. I'll have another look!
Jan 10, 2013 at 12:16 comment added Tim Dokchitser Hi Dave, did you look at Kisilevsky's paper "Ranks of elliptic curves in cubic extensions"? (In Number Theory, Analysis and Geometry, D. Goldfeld, J. Jorgenson, P. Jones, D. Ramakrishnan, K. A. Ribet, J. Tate, eds., New York, Springer, 2012). There he proves various rank growth results in general cubic extensions. Perhaps he has some precise growth conjectures there as well?
Jan 10, 2013 at 9:50 history edited Dave M da C CC BY-SA 3.0
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Jan 10, 2013 at 0:36 answer added Felipe Voloch timeline score: 2
Jan 9, 2013 at 16:40 history asked Dave M da C CC BY-SA 3.0