Serre's Uniformity Conjecture for Elliptic Curves with Rational Cyclic Isogenies

2017/02/07 by Lemos, Pedro · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1702.01985

Abstract

Let E be an elliptic curve over ℚ such that End_ℚ(E)=ℤ and which admits a non-trivial cyclic ℚ-isogeny. We prove that, for p>37, the residual mod p Galois representation ρ_E,p:G_ℚ\rightarrowGL₂(\mathbbF_p) is surjective.

Cited by

• The possible adelic indices for elliptic curves admitting a rational cyclic isogeny
• Effective open image theorem and a Linnik type problem for elliptic curves

Related

• New isogenies of elliptic curves over number fields
• Serre's uniformity question and proper subgroups of C_ns⁺(p)
• Some cases of Serre's uniformity problem
• The possible adelic indices for elliptic curves admitting a rational cyclic isogeny
• Improved bounds for Serre's open image theorem