Torsion of Elliptic Curves Over Real Quadratic Fields of Smallest Discriminant

Naba Kanta Sarma ()
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Naba Kanta Sarma: Assam University, Silchar, Cachar

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 161-169

Abstract: Abstract In [9] and [10], Filip Najman examined the torsion of elliptic curves over the number fields $$\mathbb{Q}\left( {\sqrt { - 1} } \right)$$ ℚ ( − 1 ) and $$\mathbb{Q}\left( {\sqrt { - 3} } \right)$$ ℚ ( − 3 ) . In this paper, we study the torsion structures of elliptic curves over the real quadratic number fields $$\mathbb{Q}\left( {\sqrt 2 } \right)$$ ℚ ( 2 ) and $$\mathbb{Q}\left( {\sqrt 5 } \right)$$ ℚ ( 5 ) , which have the smallest discriminants among all real quadratic fields $$\mathbb{Q}\left( {\sqrt d } \right)$$ ℚ ( d ) with d ≢ 1 mod 4 and d ≡ 1 mod 4 respectively.

Keywords: Elliptic curve; Torsion subgroup; cusp; discriminant (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0314-y

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