curve over the rational numbers
C19257
concept
A curve over the rational numbers is an algebraic curve defined by polynomial equations with rational coefficients, considered together with its set of rational solutions and their arithmetic properties.
All labels observed (2)
| Label | Occurrences |
|---|---|
| curve over the rational numbers canonical | 1 |
| plane cubic curve | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: curve over the rational numbers
Generated description
A curve over the rational numbers is an algebraic curve defined by polynomial equations with rational coefficients, considered together with its set of rational solutions and their arithmetic properties.
Instances (2)
| Instance | Via concept surface |
|---|---|
| Fermat curve | — |
| Mordell curve | plane cubic curve |