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 (36 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
14.36-5.0.6-18-18.1	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,11,3,10,2,12)\cdots(25,35,27,34,26,36),\ldots$
14.36-5.0.6-18-18.2	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,11,3,10,2,12)\cdots(25,35,27,34,26,36),\ldots$
14.36-5.0.6-18-18.3	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,11,3,10,2,12)\cdots(25,35,27,34,26,36),\ldots$
14.36-5.0.6-18-18.4	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,11,3,10,2,12)\cdots(25,35,27,34,26,36),\ldots$
14.36-5.0.6-18-18.5	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,11,3,10,2,12)\cdots(25,35,27,34,26,36),\ldots$
14.36-5.0.6-18-18.6	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,11,3,10,2,12)\cdots(25,35,27,34,26,36),\ldots$
14.36-5.0.6-18-18.7	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,12,2,10,3,11)\cdots(25,36,26,34,27,35),\ldots$
14.36-5.0.6-18-18.8	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,12,2,10,3,11)\cdots(25,36,26,34,27,35),\ldots$
14.36-5.0.6-18-18.9	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,12,2,10,3,11)\cdots(25,36,26,34,27,35),\ldots$
14.36-5.0.6-18-18.10	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,12,2,10,3,11)\cdots(25,36,26,34,27,35),\ldots$
14.36-5.0.6-18-18.11	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,12,2,10,3,11)\cdots(25,36,26,34,27,35),\ldots$
14.36-5.0.6-18-18.12	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,12,2,10,3,11)\cdots(25,36,26,34,27,35),\ldots$
14.36-5.0.6-18-18.13	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,20,3,19,2,21)\cdots(16,35,18,34,17,36),\ldots$
14.36-5.0.6-18-18.14	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,20,3,19,2,21)\cdots(16,35,18,34,17,36),\ldots$
14.36-5.0.6-18-18.15	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,20,3,19,2,21)\cdots(16,35,18,34,17,36),\ldots$
14.36-5.0.6-18-18.16	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,20,3,19,2,21)\cdots(16,35,18,34,17,36),\ldots$
14.36-5.0.6-18-18.17	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,20,3,19,2,21)\cdots(16,35,18,34,17,36),\ldots$
14.36-5.0.6-18-18.18	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,20,3,19,2,21)\cdots(16,35,18,34,17,36),\ldots$
14.36-5.0.6-18-18.19	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,21,2,19,3,20)\cdots(16,36,17,34,18,35),\ldots$
14.36-5.0.6-18-18.20	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,21,2,19,3,20)\cdots(16,36,17,34,18,35),\ldots$
14.36-5.0.6-18-18.21	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,21,2,19,3,20)\cdots(16,36,17,34,18,35),\ldots$
14.36-5.0.6-18-18.22	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,21,2,19,3,20)\cdots(16,36,17,34,18,35),\ldots$
14.36-5.0.6-18-18.23	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,21,2,19,3,20)\cdots(16,36,17,34,18,35),\ldots$
14.36-5.0.6-18-18.24	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,21,2,19,3,20)\cdots(16,36,17,34,18,35),\ldots$
14.36-5.0.6-18-18.25	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,29,3,28,2,30)\cdots(16,26,18,25,17,27),\ldots$
14.36-5.0.6-18-18.26	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,29,3,28,2,30)\cdots(16,26,18,25,17,27),\ldots$
14.36-5.0.6-18-18.27	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,29,3,28,2,30)\cdots(16,26,18,25,17,27),\ldots$
14.36-5.0.6-18-18.28	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,29,3,28,2,30)\cdots(16,26,18,25,17,27),\ldots$
14.36-5.0.6-18-18.29	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,29,3,28,2,30)\cdots(16,26,18,25,17,27),\ldots$
14.36-5.0.6-18-18.30	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,29,3,28,2,30)\cdots(16,26,18,25,17,27),\ldots$
14.36-5.0.6-18-18.31	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,30,2,28,3,29)\cdots(16,27,17,25,18,26),\ldots$
14.36-5.0.6-18-18.32	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,30,2,28,3,29)\cdots(16,27,17,25,18,26),\ldots$
14.36-5.0.6-18-18.33	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,30,2,28,3,29)\cdots(16,27,17,25,18,26),\ldots$
14.36-5.0.6-18-18.34	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,30,2,28,3,29)\cdots(16,27,17,25,18,26),\ldots$
14.36-5.0.6-18-18.35	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,30,2,28,3,29)\cdots(16,27,17,25,18,26),\ldots$
14.36-5.0.6-18-18.36	$14$	$0$	$C_2\times C_{18}$	$36$	$0$	$[ 0; 6, 18, 18 ]$	$(1,30,2,28,3,29)\cdots(16,27,17,25,18,26),\ldots$

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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.