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
3.8-2.0.2-2-4-4.7	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.10	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.4	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.2	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.8	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.12	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-2.0.2-2-4-4.3	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.1	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.9	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.11	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-2.0.2-2-4-4.5	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.6	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.4-4-4-4.1	$5$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,5,2,6)(3,7,4,8),\ldots$
5.8-2.0.4-4-4-4.3	$5$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,5,2,6)(3,7,4,8),\ldots$
5.8-2.0.4-4-4-4.2	$5$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,5,2,6)(3,7,4,8),\ldots$
5.8-2.0.4-4-4-4.4	$5$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,6,2,5)(3,8,4,7),\ldots$
5.8-2.0.4-4-4-4.5	$5$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,6,2,5)(3,8,4,7),\ldots$
5.8-2.0.2-2-2-4-4.6	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.21	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
5.8-2.0.2-2-2-4-4.5	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.19	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.3	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.18	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.17	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.16	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.20	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.15	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.22	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
5.8-2.0.2-2-2-4-4.13	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.14	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.12	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.1	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.9	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.2	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.4	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.8	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.10	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.7	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.11	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-2.0.2-4-4-4-4.3	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-2.0.2-4-4-4-4.1	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-2.0.2-4-4-4-4.19	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-2.0.2-4-4-4-4.18	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-2.0.2-4-4-4-4.16	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-2.0.2-4-4-4-4.14	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-2.0.2-4-4-4-4.20	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-2.0.2-4-4-4-4.13	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7),\ldots$
7.8-2.0.2-4-4-4-4.12	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-2.0.2-4-4-4-4.11	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$
7.8-2.0.2-4-4-4-4.10	$7$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8),\ldots$

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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.