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 (48 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
14.16-1.0.8-8-16-16.40	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,8,4,6,2,7,3,5)(9,16,12,14,10,15,11,13),\ldots$
14.16-1.0.8-8-16-16.14	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.15	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.16	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.21	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.22	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.23	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.24	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.33	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.8-8-16-16.34	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.8-8-16-16.35	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.8-8-16-16.36	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.8-8-16-16.37	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,8,4,6,2,7,3,5)(9,16,12,14,10,15,11,13),\ldots$
14.16-1.0.8-8-16-16.38	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,8,4,6,2,7,3,5)(9,16,12,14,10,15,11,13),\ldots$
14.16-1.0.8-8-16-16.39	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,8,4,6,2,7,3,5)(9,16,12,14,10,15,11,13),\ldots$
14.16-1.0.8-8-16-16.13	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.1	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.2	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.3	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.4	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.5	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.6	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.7	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.8	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.9	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.10	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.11	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.12	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,5,3,7,2,6,4,8)(9,13,11,15,10,14,12,16),\ldots$
14.16-1.0.8-8-16-16.17	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.18	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.19	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.20	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.25	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.26	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.27	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.28	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,7,4,5,2,8,3,6)(9,15,12,13,10,16,11,14),\ldots$
14.16-1.0.8-8-16-16.29	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.8-8-16-16.30	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.8-8-16-16.31	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.8-8-16-16.32	$14$	$0$	$C_{16}$	$16$	$1$	$[ 0; 8, 8, 16, 16 ]$	$(1,6,3,8,2,5,4,7)(9,14,11,16,10,13,12,15),\ldots$
14.16-1.0.2-2-4-16-16.1	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-1.0.2-2-4-16-16.2	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-1.0.2-2-4-16-16.3	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-1.0.2-2-4-16-16.4	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-1.0.2-2-4-16-16.5	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-1.0.2-2-4-16-16.6	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-1.0.2-2-4-16-16.7	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-1.0.2-2-4-16-16.8	$14$	$0$	$C_{16}$	$16$	$2$	$[ 0; 2, 2, 4, 16, 16 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$

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Overview	Random
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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 $\F_{q}$

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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.