The rank and generators of Kihara’s elliptic curve with torsion $\mathbf{Z}/4\mathbf{Z}$ over $\mathbf{Q}(t)$

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Andrej Dujella¹  Ivica Gusić²  Petra Tadić³ 

[1] Department of Mathematics, University of Zagreb;Faculty of Chemical Engin. and Techn., University of Zagreb;Department of Economics and Tourism, Juraj Dobrila University of Pula

关键词: Elliptic curve;    specialization homomorphism;    rank;    torsion;    generators;    mwrank.;   

DOI  :  10.3792/pjaa.91.105

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

For the elliptic curve $E$ over $\mathbf{Q}(t)$ found by Kihara, with torsion group $\mathbf{Z}/4\mathbf{Z}$ 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 $E(\mathbf{Q}(t))$.

【 授权许可】

Unknown