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MR2386235 (2010e:11116) 11U05 (03B25 03C07 11G05)
Shlapentokh, Alexandra Elliptic curves retaining their rank in finite extensions and Hilbert's tenth problem for rings of algebraic numbers. Trans. Amer. Math. Soc. 360 (2008), no. 7, 3541–3555.
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