High Rank Elliptic Curves with Torsion Z/2z× Z/4z Induced by Diophantine Triples
نویسنده
چکیده
We construct an elliptic curve over the eld of rational functions with torsion group Z/2Z × Z/4Z and rank equal to 4, and an elliptic curve over Q with the same torsion group and rank 9. Both results improve previous records for ranks of curves of this torsion group. They are obtained by considering elliptic curves induced by Diophantine triples.
منابع مشابه
Diophantine Triples and Construction of High-rank Elliptic Curves over Q with Three Non-trivial 2-torsion Points
An open question is whether B(F ) < ∞. The examples of Martin-McMillen and Fermigier [8] show that B(0) ≥ 23 and B(Z/2Z) ≥ 14. It follows from results of Montgomery [18] and AtkinMorain [1] that Br(F ) ≥ 1 for all torsion groups F . Kihara [11] proved that Br(0) ≥ 14 and Fermigier [8] that Br(Z/2Z) ≥ 8. Recently, Kihara [12] and Kulesz [14] proved using parametrization by Q(t) and Q(t1, t2, t3,...
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