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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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
3.8-5.0.2-2-2-2-2.2	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.23	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.19	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.8	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.3	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.13	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.7	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.17	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.20	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.10	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.28	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-5.0.2-2-2-2-2.26	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-5.0.2-2-2-2-2.25	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-5.0.2-2-2-2-2.24	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.6	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.5	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.9	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.15	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.27	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-5.0.2-2-2-2-2.4	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.1	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.18	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.16	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.11	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.21	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.14	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-5.0.2-2-2-2-2.22	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.12	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.22	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.19	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.18	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.17	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.16	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.14	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.60	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.58	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.54	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.13	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.12	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.52	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.51	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.49	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.11	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.48	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.47	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.53	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.46	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.42	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.9	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.40	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$

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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.