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 (45 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
12.9-1.0.9-9-9-9-9.1	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.2	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.3	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.4	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.5	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.6	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.7	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.8	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.9	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.10	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.11	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.12	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.13	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.14	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.15	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,4,7,2,5,8,3,6,9),\ldots$
12.9-1.0.9-9-9-9-9.16	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.17	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.18	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.19	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.20	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.21	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.22	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.23	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,7,5,3,9,4,2,8,6),\ldots$
12.9-1.0.9-9-9-9-9.24	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,5,9,2,6,7,3,4,8),\ldots$
12.9-1.0.9-9-9-9-9.25	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,5,9,2,6,7,3,4,8),\ldots$
12.9-1.0.9-9-9-9-9.26	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,5,9,2,6,7,3,4,8),\ldots$
12.9-1.0.9-9-9-9-9.27	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,5,9,2,6,7,3,4,8),\ldots$
12.9-1.0.9-9-9-9-9.28	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,8,4,3,7,6,2,9,5),\ldots$
12.9-1.0.9-9-9-9-9.29	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,8,4,3,7,6,2,9,5),\ldots$
12.9-1.0.9-9-9-9-9.30	$12$	$0$	$C_9$	$9$	$2$	$[ 0; 9, 9, 9, 9, 9 ]$	$(1,6,8,2,4,9,3,5,7),\ldots$
12.9-1.0.3-3-3-3-9-9.1	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.2	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.3	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.4	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.5	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.6	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.7	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.8	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.9	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.10	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.11	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.12	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,2,3)(4,5,6)(7,8,9),\ldots$
12.9-1.0.3-3-3-3-9-9.13	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$
12.9-1.0.3-3-3-3-9-9.14	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$
12.9-1.0.3-3-3-3-9-9.15	$12$	$0$	$C_9$	$9$	$3$	$[ 0; 3, 3, 3, 3, 9, 9 ]$	$(1,3,2)(4,6,5)(7,9,8),\ldots$

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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.