Frey curve
E921623
The Frey curve is an elliptic curve construction introduced by Gerhard Frey that played a pivotal role in linking Fermat’s Last Theorem to the modularity conjecture, ultimately contributing to its proof.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Frey curve canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T11365700 — 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: Frey curve Context triple: [Gerhard Frey, notableWork, Frey curve]
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A.
Schoen
Schoen is a German-origin surname borne by various notable individuals in fields such as mathematics, science, and the arts.
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B.
Frederickson
Frederickson is a surname of likely Scandinavian origin borne by various individuals, including film producer Gray Frederickson.
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C.
Grafh
Grafh is an American rapper from Queens, New York, known for his gritty lyricism and work in the underground hip-hop scene.
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D.
Frachey
Frachey is a small alpine village in Italy’s Aosta Valley, known as a gateway to the Monterosa Ski area.
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E.
Wuscfrea
Wuscfrea was a little-known early medieval Northumbrian prince, known primarily as a son of King Edwin of Northumbria.
- 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: Frey curve Target entity description: The Frey curve is an elliptic curve construction introduced by Gerhard Frey that played a pivotal role in linking Fermat’s Last Theorem to the modularity conjecture, ultimately contributing to its proof.
-
A.
Schoen
Schoen is a German-origin surname borne by various notable individuals in fields such as mathematics, science, and the arts.
-
B.
Frederickson
Frederickson is a surname of likely Scandinavian origin borne by various individuals, including film producer Gray Frederickson.
-
C.
Grafh
Grafh is an American rapper from Queens, New York, known for his gritty lyricism and work in the underground hip-hop scene.
-
D.
Frachey
Frachey is a small alpine village in Italy’s Aosta Valley, known as a gateway to the Monterosa Ski area.
-
E.
Wuscfrea
Wuscfrea was a little-known early medieval Northumbrian prince, known primarily as a son of King Edwin of Northumbria.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
elliptic curve
ⓘ
mathematical object ⓘ |
| appearsIn | proof strategy for Fermat’s Last Theorem via modularity lifting ⓘ |
| associatedWith |
Fermat’s Last Theorem
ⓘ
linked to:
Fermat's Last Theorem
Taniyama–Shimura–Weil conjecture ⓘ modularity conjecture ⓘ |
| centralIdea | derive contradiction between non-modularity and modularity theorem ⓘ |
| consideredBy |
Jean-Pierre Serre
ⓘ
Ken Ribet ⓘ |
| constructedFrom | putative solution of Fermat’s equation a^p + b^p = c^p with p > 2 ⓘ |
| constructionType | elliptic curve construction ⓘ |
| definedOver | rational numbers ⓘ |
| field |
arithmetic geometry
ⓘ
number theory ⓘ |
| hasProperty |
conductor depending on the Fermat triple
ⓘ
semistable ⓘ would be non-modular if a non-trivial Fermat solution existed ⓘ |
| inspiredResult |
Ribet’s level-lowering theorem
ⓘ
linked to:
Ribet's theorem
|
| introducedBy | Gerhard Frey ⓘ |
| introducedInDecade | 1980s ⓘ |
| motivated | link between Fermat’s Last Theorem and modularity conjecture ⓘ |
| namedAfter | Gerhard Frey ⓘ |
| playedRoleIn |
Ribet’s theorem
ⓘ
linked to:
Ribet's theorem
Wiles’s proof of Fermat’s Last Theorem ⓘ |
| relatedConcept |
Galois representation
ⓘ
linked to:
Galois representations
epsilon conjecture of Serre ⓘ
linked to:
Serre’s conjecture on Galois representations
modular elliptic curve ⓘ |
| studiedIn | Diophantine equations ⓘ |
| typicalEquationForm | y^2 = x(x - a^p)(x + b^p) ⓘ |
| usedInProofOf |
Fermat’s Last Theorem
ⓘ
linked to:
Fermat's Last Theorem
|
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: Frey curve Description of subject: The Frey curve is an elliptic curve construction introduced by Gerhard Frey that played a pivotal role in linking Fermat’s Last Theorem to the modularity conjecture, ultimately contributing to its proof.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.