PreprintCC BY 4.0arXiv
On the Iwasawa invariants of admissible quadratic twists of elliptic curves at ordinary Eisenstein primes
Abstract
We study the Iwasawa μ- and λ-invariants of quadratic twists of rational elliptic curves at Eisenstein primes p≥ 3. We verify Greenberg's μ=0 conjecture for all such twists, which gives an Euler system free proof of Mazur's cotorsion conjecture, and study the λ-invariants when the twist is admissible in the sense of [GV00]. As a consequence, we prove the cyclotomic Iwasawa Main Conjecture and obtain the p-part BSD formulae in rank $0$ for admissible twists under mild conditions, covering many elliptic curves of potentially ordinary reduction.
Related
- Iwasawa invariants of sharp/flat $2$-adic L-functions for quadratic twists of elliptic curves
- On Greenberg's conjecture for rational elliptic curves at Eisenstein primes
- Spectral L2-bounds on Eisenstein series and Diophantine properties of quadratic forms
- Higher Schwarzians of Elliptic Double Covers and Eisenstein--Kronecker Functions
- Nakajima-extremal Artin--Schreier covers of ordinary elliptic curves in characteristic $2$
BibTeX
@misc{yin2026iwasawa,
title = {{On the Iwasawa invariants of admissible quadratic twists of elliptic curves at ordinary Eisenstein primes}},
author = {Mulun Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42137},
eprint = {2610.42137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42137},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Iwasawa invariants of admissible quadratic twists of elliptic curves at ordinary Eisenstein primes
AU - Mulun Yin
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42137
UR - https://arxiv.org/abs/2610.42137
AB - We study the Iwasawa μ- and λ-invariants of quadratic twists of rational elliptic curves at Eisenstein primes p≥ 3. We verify Greenberg's μ=0 conjecture for all such twists, which gives an Euler system free proof of Mazur's cotorsion conjecture, and study the λ-invariants when the twist is admissible in the sense of [GV00]. As a consequence, we prove the cyclotomic Iwasawa Main Conjecture and obtain the p-part BSD formulae in rank $0$ for admissible twists under mild conditions, covering many elliptic curves of potentially ordinary reduction.
ER -