Geodesic
A NOTE ON HIGHER TWISTS OF ELLIPTIC CURVES
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 371-381

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DOI

We show that for any pair of elliptic curves E1, E2 over Q with j-invariant equal to 0, we can find a polynomial D ∈ Z[u, v] such that the cubic twists of the curves E1, E2 by D(u, v) have positive rank over Q(u, v). We also prove that for any quadruple of pairwise distinct elliptic curves Ei, i = 1, 2, 3, 4, with j-invariant j = 0, there exists a polynomial D ∈ Z[u] such that the sextic twists of Ei, i = 1, 2, 3, 4, by D(u) have positive rank. A similar result is proved for quadruplets of elliptic curves with j-invariant j = 1, 728.
DOI : 10.1017/S0017089510000066
Mots-clés : 11G05 
ULAS, MACIEJ. A NOTE ON HIGHER TWISTS OF ELLIPTIC CURVES. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 371-381. doi: 10.1017/S0017089510000066
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     journal = {Glasgow mathematical journal},
     pages = {371--381},
     year = {2010},
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     doi = {10.1017/S0017089510000066},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000066/}
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