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 (26 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
13.9-1.0.3-3-3-9-9-9.2	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.3	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.1	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.4	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.5	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.6	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.7	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.8	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.9	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.10	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.11	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.12	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.13	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.14	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.15	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.16	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.17	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.18	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.19	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.20	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
13.9-1.0.3-3-3-9-9-9.21	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$
13.9-1.0.3-3-3-9-9-9.22	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$
13.9-1.0.3-3-3-9-9-9.23	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$
13.9-1.0.3-3-3-9-9-9.24	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$
13.9-1.0.3-3-3-9-9-9.25	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$
13.9-1.0.3-3-3-9-9-9.26	$13$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 9, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$

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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.