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 high ranks 10 and 11.
Keywords: 14H52; 2010 MSC: 11G05; Elliptic curve; rank; torsion group.