Elkies trinomial curves [SEP] named after
Elkies trinomial curves
In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials giving an extension of Q with particular Galois groups.
One curve, C, gives Galois group PSL(2,7) from a polynomial of degree seven, and the other, C, gives Galois group AL(8), the semidirect product of a 2-elementary group of order eight acted on by PSL(2, 7), giving a transitive permutation subgroup of the symmetric group
Cubic curve
- Elliptic curve
- Watt's curve
Algebraic curves Curves with genus greater than one.
- Bolza surface (genus 2)
- Klein quartic (genus 3)
- Bring's curve (genus 4)
- Macbeath surface (genus 7)
- Butterfly curve (algebraic) (genus 7)
Algebraic curves Curve families with variable genus.
- Polynomial lemniscate
- Fermat curve
- Sinusoidal spiral
- Superellipse
- Hurwitz surface
- Elkies trinomial curves
- Hyperelliptic curve