Introduction to Elliptic Curves and Modular Forms
E831065
Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Introduction to Elliptic Curves and Modular Forms canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9931756 — 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: Introduction to Elliptic Curves and Modular Forms Context triple: [Neal Koblitz, authorOf, Introduction to Elliptic Curves and Modular Forms]
-
A.
Lectures on Elliptic Curves
Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
-
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.
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.
-
D.
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.
-
E.
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.
- 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: Introduction to Elliptic Curves and Modular Forms Target entity description: Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
-
A.
Lectures on Elliptic Curves
Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
-
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.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
graduate-level textbook
ⓘ
mathematics textbook ⓘ monograph ⓘ |
| abbreviation |
GTM 97
ⓘ
linked to:
GTM
|
| author | Neal Koblitz ⓘ |
| edition |
first edition 1984
ⓘ
revised edition ⓘ second edition 1993 ⓘ |
| field |
algebraic geometry
ⓘ
arithmetic geometry ⓘ elliptic curves ⓘ modular forms ⓘ number theory ⓘ |
| focus |
analytic properties of modular forms
ⓘ
arithmetic properties of elliptic curves ⓘ connections between elliptic curves and modular forms ⓘ |
| language | English ⓘ |
| level | graduate ⓘ |
| prerequisite |
basic abstract algebra
ⓘ
undergraduate complex analysis ⓘ undergraduate real analysis ⓘ |
| publisher | Springer ⓘ |
| relatedTo |
Birch and Swinnerton-Dyer conjecture
ⓘ
linked to:
Birch and Swinnerton-Dyer Conjecture
Fermat’s Last Theorem ⓘ
linked to:
Fermat's Last Theorem
Taniyama–Shimura–Weil conjecture ⓘ |
| series | Graduate Texts in Mathematics ⓘ |
| topic |
Diophantine equations
ⓘ
Eisenstein series ⓘ Galois representations associated to elliptic curves ⓘ Hasse’s theorem on elliptic curves ⓘ
linked to:
Hasse bound for elliptic curves
Hecke operators ⓘ L-functions of elliptic curves ⓘ Mordell–Weil theorem ⓘ Weierstrass equations ⓘ
linked to:
Weierstrass form
applications to cryptography ⓘ basic theory of elliptic curves ⓘ complex multiplication ⓘ cusp forms ⓘ elliptic curves over finite fields ⓘ elliptic curves over number fields ⓘ group law on elliptic curves ⓘ modular curves ⓘ modular forms of one variable ⓘ q-expansions of modular forms ⓘ reduction of elliptic curves modulo primes ⓘ torsion points on elliptic curves ⓘ |
| usedAs |
graduate course textbook
ⓘ
reference work for researchers ⓘ |
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: Introduction to Elliptic Curves and Modular Forms Description of subject: Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.