Bring's curve is a genus 4 curve with automorphism group $S_5$, the largest automorphism group of any curve of genus 4. It is the corresponding Riemann surface of the small stellated dodecahedron. A model for it is $$ B \subset {\bf P}^4: \sum_{i=1}^5 x_i = \sum_{i=1}^5 x_i^2 = \sum_{i=1}^5 x_i^3 = 0.$$
Family Information
Genus: | $4$ |
Dimension of the family: | $0$ |
Cover
Quotient genus: | $0$ |
Number of branch points: | $3$ |
Signature: | $[ 0; 2, 4, 5 ]$ |
Group
Name: | $S_5$ |
Identifier: | $[120,34]$ |
Conjugacy class(es) of Refined passports
Refined passport label | Lists of conjugacy classes |
---|---|
4.120-34.0.2-4-5.1 | 2, 5, 6 |