LMFDB - Family of higher genus curves with automorphisms search results

Refine search

Genus	Dimension of the family	Group order	Hyperelliptic curves	Full automorphism group

Quotient genus	Signature	Group identifier	Cyclic trigonal curves

		Sort order	Select

Results (47 matches)

Download displayed columns for results to

Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
2.16-8.0.2-4-8.1	$2$	$0$	$\SD_{16}$	$16$	$0$	$[ 0; 2, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
2.16-8.0.2-4-8.2	$2$	$0$	$\SD_{16}$	$16$	$0$	$[ 0; 2, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
5.16-8.0.2-2-4-4.1	$5$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
6.16-8.0.2-2-4-8.1	$6$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
6.16-8.0.2-2-4-8.2	$6$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
7.16-8.0.2-2-8-8.1	$7$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
7.16-8.0.2-2-8-8.3	$7$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
7.16-8.0.2-2-8-8.2	$7$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
8.16-8.0.2-4-4-8.1	$8$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 4, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
8.16-8.0.2-4-4-8.2	$8$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 2, 4, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
9.16-8.0.2-2-2-4-4.1	$9$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
10.16-8.0.2-2-2-4-8.2	$10$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
10.16-8.0.2-2-2-4-8.4	$10$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
10.16-8.0.2-2-2-4-8.3	$10$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
10.16-8.0.2-2-2-4-8.1	$10$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-8.0.4-4-8-8.3	$11$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,9,2,10)(3,12,4,11)(5,15,6,16)(7,13,8,14),\ldots$
11.16-8.0.4-4-8-8.2	$11$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,9,2,10)(3,12,4,11)(5,15,6,16)(7,13,8,14),\ldots$
11.16-8.0.4-4-8-8.1	$11$	$0$	$\SD_{16}$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,9,2,10)(3,12,4,11)(5,15,6,16)(7,13,8,14),\ldots$
11.16-8.0.2-2-4-4-4.1	$11$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
11.16-8.0.2-2-2-8-8.1	$11$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-8.0.2-2-2-8-8.2	$11$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-8.0.2-2-2-8-8.3	$11$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
12.16-8.0.2-2-4-4-8.2	$12$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 4, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
12.16-8.0.2-2-4-4-8.1	$12$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 4, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-8.0.2-2-4-8-8.1	$13$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
13.16-8.0.2-2-4-8-8.3	$13$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
13.16-8.0.2-2-4-8-8.2	$13$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
13.16-8.0.2-2-2-2-4-4.1	$13$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-8.0.2-2-2-2-4-4.2	$13$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
14.16-8.0.2-4-4-4-8.1	$14$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 4, 4, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
14.16-8.0.2-4-4-4-8.2	$14$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 4, 4, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
14.16-8.0.2-4-4-4-8.3	$14$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 4, 4, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
14.16-8.0.2-4-4-4-8.4	$14$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 4, 4, 4, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
14.16-8.0.2-2-2-2-4-8.4	$14$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-8.0.2-2-2-2-4-8.1	$14$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-8.0.2-2-2-2-4-8.2	$14$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-8.0.2-2-2-2-4-8.3	$14$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-4-4-8-8.3	$15$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-4-4-8-8.2	$15$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-4-4-8-8.1	$15$	$0$	$\SD_{16}$	$16$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-2-2-2-8-8.6	$15$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
15.16-8.0.2-2-2-2-8-8.1	$15$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-2-2-4-4-4.1	$15$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-2-2-2-8-8.3	$15$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-2-2-2-8-8.2	$15$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-8.0.2-2-2-2-8-8.4	$15$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$
15.16-8.0.2-2-2-2-8-8.5	$15$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15),\ldots$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (47 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.