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arxiv: 1410.6919 · v1 · pith:IJRGDUZ4new · submitted 2014-10-25 · 🧮 math.NT · math.AG

The rank and generators of Kihara's elliptic curve with torsion mathbb{Z}/4mathbb{Z} over mathbb{Q}(t)

classification 🧮 math.NT math.AG
keywords mathbbrankcurveellipticgeneratorskiharatorsioncurrent
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For the elliptic curve $E$ over $\mathbb{Q}(t)$ found by Kihara, with torsion group $\mathbb{Z}/4\mathbb{Z}$ and rank $\geq 5$, which is the current record for the rank of such curves, by using a suitable injective specialization, we determine exactly the rank and generators of $E(\mathbb{Q}(t))$.

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