Cassels, J. W. S., Lectures on Elliptic Curves
E654587
"Cassels, J. W. S., Lectures on Elliptic Curves" is a classic introductory monograph that systematically develops the arithmetic theory of elliptic curves, widely used as a foundational text in number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Cassels, J. W. S., Lectures on Elliptic Curves canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7304643 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cassels, J. W. S., Lectures on Elliptic Curves Context triple: [J. W. S. Cassels, hasBibliographyItem, Cassels, J. W. S., Lectures on Elliptic Curves]
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A.
Cassels–Fröhlich: Algebraic Number Theory
Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
-
B.
A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
-
C.
Three Lectures on Fermat's Last Theorem
"Three Lectures on Fermat's Last Theorem" is a classic expository work in number theory in which Louis Mordell surveys the history, methods, and partial results surrounding Fermat's Last Theorem prior to its eventual proof.
-
D.
Hasse bound for elliptic curves
The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
-
E.
Neukirch: Algebraic Number Theory
"Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cassels, J. W. S., Lectures on Elliptic Curves Target entity description: "Cassels, J. W. S., Lectures on Elliptic Curves" is a classic introductory monograph that systematically develops the arithmetic theory of elliptic curves, widely used as a foundational text in number theory.
-
A.
Cassels–Fröhlich: Algebraic Number Theory
Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
-
B.
A Course in Arithmetic
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
-
C.
Three Lectures on Fermat's Last Theorem
"Three Lectures on Fermat's Last Theorem" is a classic expository work in number theory in which Louis Mordell surveys the history, methods, and partial results surrounding Fermat's Last Theorem prior to its eventual proof.
-
D.
Hasse bound for elliptic curves
The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
-
E.
Neukirch: Algebraic Number Theory
"Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ textbook ⓘ |
| author | J. W. S. Cassels ⓘ |
| contains |
exercises
ⓘ
theorems with proofs ⓘ worked examples ⓘ |
| emphasis |
Diophantine methods
ⓘ
arithmetic properties of elliptic curves ⓘ rational solutions to polynomial equations ⓘ |
| field |
arithmetic geometry
ⓘ
number theory ⓘ |
| focusesOn |
Diophantine equations
ⓘ
Mordell–Weil theorem ⓘ arithmetic of elliptic curves ⓘ descent on elliptic curves ⓘ elliptic curves over number fields ⓘ heights on elliptic curves ⓘ rational points on elliptic curves ⓘ torsion points on elliptic curves ⓘ |
| genre | academic monograph ⓘ |
| influenced | later textbooks on elliptic curves ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
researchers in number theory ⓘ |
| isConsidered | classic introduction to elliptic curves ⓘ |
| isUsedAs |
foundational text for arithmetic of elliptic curves
ⓘ
standard reference in number theory courses ⓘ |
| language | English ⓘ |
| level | introductory graduate ⓘ |
| mainSubject | elliptic curves ⓘ |
| prerequisite |
basic algebra
ⓘ
elementary number theory ⓘ some algebraic number theory ⓘ |
| reputation |
concise
ⓘ
rigorous ⓘ standard reference in arithmetic geometry ⓘ |
| structure | systematic development of arithmetic theory of elliptic curves ⓘ |
| topic |
Galois representations of elliptic curves
ⓘ
Weierstrass equations ⓘ
linked to:
Weierstrass form
algebraic number theory ⓘ elliptic curves over the rationals ⓘ group law on elliptic curves ⓘ local fields and elliptic curves ⓘ reduction of elliptic curves modulo primes ⓘ |
| usedIn |
graduate seminars on elliptic curves
ⓘ
self-study by number theorists ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Cassels, J. W. S., Lectures on Elliptic Curves Description of subject: "Cassels, J. W. S., Lectures on Elliptic Curves" is a classic introductory monograph that systematically develops the arithmetic theory of elliptic curves, widely used as a foundational text in number theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.