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PreprintCC BY 4.0arXiv

Computing the Iwasawa μ-Invariants for Elliptic Curves over ℤ2-Extensions

  • Zichao Lin
  • Mulun Yin
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Abstract

Let E be an elliptic curve defined over rational numbers. Further assume E has good ordinary reduction at p=2 and E[4] is reducible as a GQ-representation. In this paper, we offer sufficient and necessary computational criteria for the algebraic Iwasawa μ-invariant over the cyclotomic ℤ2-extension of rational number to be $0$, $1$ or ≥ 2. We also show that elliptic curves with isomorphic mod-$4$ representations have algebraic μ-invariant equal to $0$ if one of the curves does.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026computing,
  title = {{Computing the Iwasawa $μ$-Invariants for Elliptic Curves over $\mathbbZ_2$-Extensions}},
  author = {Zichao Lin and Mulun Yin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31532},
  eprint = {2609.31532},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31532},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Computing the Iwasawa μ-Invariants for Elliptic Curves over ℤ_2-Extensions
AU  - Zichao Lin
AU  - Mulun Yin
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31532
UR  - https://arxiv.org/abs/2609.31532
AB  - Let E be an elliptic curve defined over rational numbers. Further assume E has good ordinary reduction at p=2 and E[4] is reducible as a G_Q-representation. In this paper, we offer sufficient and necessary computational criteria for the algebraic Iwasawa μ-invariant over the cyclotomic ℤ_2-extension of rational number to be $0$, $1$ or ≥ 2. We also show that elliptic curves with isomorphic mod-$4$ representations have algebraic μ-invariant equal to $0$ if one of the curves does.
ER  -