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	Cyclic trigonal	Generating vectors
2.2-1.0.2-2-2-2-2-2.1	$2$	$0$	$C_2$	$2$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2),\ldots$
3.2-1.2.0.1	$3$	$2$	$C_2$	$2$	$3$	$[ 2; -]$			$(1,2),\ldots$
3.4-2.0.2-2-2-2-2-2.2	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.3	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.7	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,3)(2,4),\ldots$
3.4-2.0.2-2-2-2-2-2.4	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.6	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,3)(2,4),\ldots$
3.4-2.0.2-2-2-2-2-2.5	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.1	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
4.3-1.0.3-3-3-3-3-3.1	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
4.3-1.0.3-3-3-3-3-3.2	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
4.3-1.0.3-3-3-3-3-3.3	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$		✓	$(1,3,2),\ldots$
4.3-1.1.3-3-3.2	$4$	$1$	$C_3$	$3$	$3$	$[ 1; 3, 3, 3 ]$			$(1,2,3),\ldots$
4.3-1.1.3-3-3.1	$4$	$1$	$C_3$	$3$	$3$	$[ 1; 3, 3, 3 ]$			$(1,2,3),\ldots$
4.3-1.2.0.1	$4$	$2$	$C_3$	$3$	$3$	$[ 2; -]$			$(1,2,3),\ldots$
4.4-1.0.2-2-2-2-4-4.1	$4$	$0$	$C_4$	$4$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
4.4-2.1.2-2-2.1	$4$	$1$	$C_2^2$	$4$	$3$	$[ 1; 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.6-1.0.2-2-2-2-2-2.1	$4$	$0$	$S_3$	$6$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,6)(3,5),\ldots$
5.4-1.0.2-2-4-4-4-4.2	$5$	$0$	$C_4$	$4$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
5.4-1.0.2-2-4-4-4-4.1	$5$	$0$	$C_4$	$4$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
5.4-1.0.2-2-4-4-4-4.3	$5$	$0$	$C_4$	$4$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
5.6-1.0.2-2-2-2-3-3.1	$5$	$0$	$S_3$	$6$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$			$(1,4)(2,6)(3,5),\ldots$
5.6-2.0.2-2-2-2-3-3.1	$5$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
5.8-5.0.2-2-2-2-2-2.28	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.26	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.21	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.25	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.34	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.38	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.27	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-3.0.2-2-2-2-2-2.2	$5$	$0$	$D_4$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.29	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.24	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.33	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.32	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.31	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.4	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.35	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.36	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.37	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.30	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.39	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-3.0.2-2-2-2-2-2.1	$5$	$0$	$D_4$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.1	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.23	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.2	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-3.0.2-2-2-2-2-2.3	$5$	$0$	$D_4$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.3	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.22	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.20	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$

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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.