Local torsion primes and the class numbers associated to an elliptic curve over ℚ

2017/03/24 by Hiranouchi, Toshiro
#11G05 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1703.08275

Abstract

Using the rank of the Mordell-Weil group E(ℚ) of an elliptic curve E over ℚ, we give a lower bound of the class number of the number field ℚ(E[pⁿ]) generated by pⁿ-division points of E when the curve E does not possess a p-adic point of order p: E(ℚ_p)[p] =0.

Related

• On the class numbers of the fields of the pⁿ-torsion points of certain elliptic curves over Q
• On the class numbers of the fields of the pⁿ-torsion points of elliptic curves over ℚ
• Elliptic surfaces over ℙ¹ and large class groups of number fields
• The Frequency of Elliptic Curves Over ℚ[i] with Fixed Torsion
• Local torsion on elliptic curves and the deformation theory of Galois representations