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High Rank Elliptic Curves with Torsion Z/4Z Induced by Kihara's Elliptic Curves

Working over the field Q(t), Kihara constructed an elliptic curve with torsion group Z/4Z and five independent rational points, showing the rank is at least five. Following his approach, we give a new infinite family of elliptic curves with torsion group Z/4Z and rank at least five. This matches the current record for such curves. In addition, we give specific examples of these curves with ranks 10 and 11.