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 155 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
7.8-5.0.2-2-2-2-2-2-2.2	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.3	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.4	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.42	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.65	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.66	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.69	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.71	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.82	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.90	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.92	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.96	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.114	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.115	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.124	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.134	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.136	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.142	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-5.0.2-2-2-2-2-2-2.148	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-5.0.2-2-2-2-2-2-2.155	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-5.0.2-2-2-2-2-2-2.1	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.5	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.7	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.9	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.10	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.11	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.12	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.13	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.16	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.19	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.20	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.22	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.26	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.27	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.29	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.31	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.35	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.58	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.75	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.77	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.79	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.84	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.107	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.119	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.120	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.123	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.127	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.129	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.21	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.38	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$

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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 $\F_{q}$

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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.