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 (1-50 of 64 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
11.16-5.0.4-4-8-8.22	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.17	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.18	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.19	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.20	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.21	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.23	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.24	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,7,2,8)(3,6,4,5)(9,15,10,16)(11,14,12,13),\ldots$
11.16-5.0.4-4-8-8.25	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,8,2,7)(3,5,4,6)(9,16,10,15)(11,13,12,14),\ldots$
11.16-5.0.4-4-8-8.26	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,8,2,7)(3,5,4,6)(9,16,10,15)(11,13,12,14),\ldots$
11.16-5.0.4-4-8-8.27	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,8,2,7)(3,5,4,6)(9,16,10,15)(11,13,12,14),\ldots$
11.16-5.0.4-4-8-8.28	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,8,2,7)(3,5,4,6)(9,16,10,15)(11,13,12,14),\ldots$
11.16-5.0.4-4-8-8.10	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.4-4-8-8.3	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.6	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.7	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.8	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.5	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.11	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.4-4-8-8.13	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.4-4-8-8.14	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.4-4-8-8.12	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.4-4-8-8.2	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.1	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.4	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16),\ldots$
11.16-5.0.4-4-8-8.9	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.4-4-8-8.16	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.4-4-8-8.15	$11$	$0$	$C_2\times C_8$	$16$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15),\ldots$
11.16-5.0.2-2-2-8-8.29	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-5.0.2-2-2-8-8.30	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-5.0.2-2-2-8-8.31	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-5.0.2-2-2-8-8.32	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-5.0.2-2-2-8-8.1	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.34	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$	✓	$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
11.16-5.0.2-2-2-8-8.35	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$	✓	$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
11.16-5.0.2-2-2-8-8.36	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$	✓	$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
11.16-5.0.2-2-2-8-8.33	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$	✓	$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
11.16-5.0.2-2-2-8-8.2	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.3	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.4	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.5	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.6	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.7	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.8	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.9	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.10	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.11	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.12	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.13	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-5.0.2-2-2-8-8.14	$11$	$0$	$C_2\times C_8$	$16$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$

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Classical	Maass
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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.