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 (33 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
12.5-1.0.5-5-5-5-5-5-5-5.5	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.6	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.7	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.8	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.9	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.10	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.11	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.12	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.13	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.14	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.15	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.16	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.17	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.18	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.19	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.20	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.21	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.22	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.23	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.24	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.25	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.26	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.1	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.2	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.3	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.4	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.27	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.28	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.29	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.30	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.31	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.32	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,4,2,5,3),\ldots$
12.5-1.0.5-5-5-5-5-5-5-5.33	$12$	$0$	$C_5$	$5$	$5$	$[ 0; 5, 5, 5, 5, 5, 5, 5, 5 ]$	$(1,4,2,5,3),\ldots$

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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 $\F_{q}$

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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.