The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Rational isogenies of prime degree
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Grothendieck, A. (1964) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684747 · Cited by 2,824
The irreducibility of the space of curves of given genus
Deligne, P., & Mumford, D. (1969) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684599 · Cited by 1,631 · cited 2×
“For a general discussion of algebraic stacks, see [ 7 ], w 4.”
BackgroundInfluentialPropri�t�s galoisiennes des points d'ordre fini des courbes elliptiques
Serre, J.-P. (1971) · Inventiones mathematicae · doi:10.1007/bf01405086 · Cited by 998
Modular curves and the Eisenstein ideal
Mazur, B. (1977) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684339 · Cited by 945
Self-citationGood Reduction of Abelian Varieties
Serre, J.-P., & Tate, J. (1968) · Annals of Mathematics · doi:10.2307/1970722 · Cited by 827
Linear Groups with an Exposition of the Galois Field Theory
Dickson, L. E., & Gillis, J. (1959) · Physics Today · doi:10.1063/1.3060528 · Cited by 653
Algorithm for determining the type of a singular fiber in an elliptic pencil
Tate, J. (1975) · Lecture notes in mathematics · doi:10.1007/bfb0097582 · Cited by 477
Groupes algébriques et corps de classes
Serre, J.-P. (1997) · Groupes algébriques et corps de classes · doi:10.3917/herm.serre.1997.02.0163 · Cited by 430
Über die Classenzahl quadratischer Zahlkörper
Siegel, C. (1935) · Acta Arithmetica · doi:10.4064/aa-1-1-83-86 · Cited by 276
Universal Bounds on the Torsion of Elliptic Curves
Kubert, D. S. (1976) · Proceedings of the London Mathematical Society · doi:10.1112/plms/s3-33.2.193 · Cited by 266
Metadata
- Authors
- Mazur, B., & Goldfeld, D.
- Venue
- Inventiones Mathematicae
- Published
- 1978-06
- Volume
- 44
- Issue
- 2
- Pages
- 129-162
- ISSN
- 0020-9910 (ISSN-L)
- 1432-1297
- OpenAlex
- W2011844852
- Cited by
- 666
- References
- 13
- FWCI
- 8.19
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Rational isogenies of prime degree. https://app.cochat.ai/papers/10.1007/bf01390348
- The paper
- Mazur, B., & Goldfeld, D. (1978). Rational isogenies of prime degree. Inventiones Mathematicae. https://doi.org/10.1007/bf01390348
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
