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 54 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
12.27-1.0.9-27-27.4	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.1	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.2	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.3	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.5	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.6	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.7	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.8	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.9	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,4,7,2,5,8,3,6,9)\cdots(19,22,25,20,23,26,21,24,27),\ldots$
12.27-1.0.9-27-27.10	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.11	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.12	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.13	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.14	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.15	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.16	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.17	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.18	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,7,5,3,9,4,2,8,6)\cdots(19,25,23,21,27,22,20,26,24),\ldots$
12.27-1.0.9-27-27.19	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.20	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.21	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.22	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.23	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.24	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.25	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.26	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.27	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,5,9,2,6,7,3,4,8)\cdots(19,23,27,20,24,25,21,22,26),\ldots$
12.27-1.0.9-27-27.28	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.29	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.30	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.31	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.32	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.33	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.34	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.35	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.36	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,8,4,3,7,6,2,9,5)\cdots(19,26,22,21,25,24,20,27,23),\ldots$
12.27-1.0.9-27-27.37	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.38	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.39	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.40	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.41	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.42	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.43	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.44	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.45	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,6,8,2,4,9,3,5,7)\cdots(19,24,26,20,22,27,21,23,25),\ldots$
12.27-1.0.9-27-27.46	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,9,6,3,8,5,2,7,4)\cdots(19,27,24,21,26,23,20,25,22),\ldots$
12.27-1.0.9-27-27.47	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,9,6,3,8,5,2,7,4)\cdots(19,27,24,21,26,23,20,25,22),\ldots$
12.27-1.0.9-27-27.48	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,9,6,3,8,5,2,7,4)\cdots(19,27,24,21,26,23,20,25,22),\ldots$
12.27-1.0.9-27-27.49	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,9,6,3,8,5,2,7,4)\cdots(19,27,24,21,26,23,20,25,22),\ldots$
12.27-1.0.9-27-27.50	$12$	$0$	$C_{27}$	$27$	$0$	$[ 0; 9, 27, 27 ]$	$(1,9,6,3,8,5,2,7,4)\cdots(19,27,24,21,26,23,20,25,22),\ldots$

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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.