LMFDB - Family of higher genus curves with automorphisms search results

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

Quotient genus	Signature	Group identifier	Cyclic trigonal curves

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Results (35 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
11.16-13.0.2-2-4-4-4.1	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-4-4-4.2	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-4-4-4.3	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-4-4-4.4	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-4-4-4.5	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-4-4-4.6	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-4-4-4.7	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.8	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.9	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.10	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.11	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.12	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.13	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.14	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.15	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.16	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.17	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-4-4-4.18	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15),\ldots$
11.16-13.0.2-2-4-4-4.19	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15),\ldots$
11.16-13.0.2-2-4-4-4.20	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15),\ldots$
11.16-13.0.2-2-4-4-4.21	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15),\ldots$
11.16-13.0.2-2-4-4-4.22	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15),\ldots$
11.16-13.0.2-2-4-4-4.23	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15),\ldots$
11.16-13.0.2-2-4-4-4.24	$11$	$0$	$D_4:C_2$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	$(1,15)(2,16)(3,14)(4,13)(5,12)(6,11)(7,9)(8,10),\ldots$
11.16-13.0.2-2-2-2-2-4.1	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-2-2-2-4.2	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-2-2-2-4.3	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-2-2-2-4.4	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-2-2-2-4.5	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-13.0.2-2-2-2-2-4.6	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-2-2-2-4.7	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-2-2-2-4.8	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-2-2-2-4.9	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-2-2-2-4.10	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-13.0.2-2-2-2-2-4.11	$11$	$0$	$D_4:C_2$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$

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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

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