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
4.2-1.0.2-2-2-2-2-2-2-2-2-2.1	$4$	$0$	$C_2$	$2$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2),\ldots$
4.2-1.1.2-2-2-2-2-2.1	$4$	$1$	$C_2$	$2$	$6$	$[ 1; 2, 2, 2, 2, 2, 2 ]$			$(1,2),\ldots$
4.2-1.2.2-2.1	$4$	$2$	$C_2$	$2$	$5$	$[ 2; 2, 2 ]$			$(1,2),\ldots$
4.3-1.0.3-3-3-3-3-3.1	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
4.3-1.0.3-3-3-3-3-3.3	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$		✓	$(1,3,2),\ldots$
4.3-1.0.3-3-3-3-3-3.2	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
4.3-1.1.3-3-3.1	$4$	$1$	$C_3$	$3$	$3$	$[ 1; 3, 3, 3 ]$			$(1,2,3),\ldots$
4.3-1.1.3-3-3.2	$4$	$1$	$C_3$	$3$	$3$	$[ 1; 3, 3, 3 ]$			$(1,2,3),\ldots$
4.3-1.2.0.1	$4$	$2$	$C_3$	$3$	$3$	$[ 2; -]$			$(1,2,3),\ldots$
4.4-1.0.2-4-4-4-4.1	$4$	$0$	$C_4$	$4$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
4.4-1.0.2-4-4-4-4.2	$4$	$0$	$C_4$	$4$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
4.4-1.0.2-2-2-2-4-4.1	$4$	$0$	$C_4$	$4$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.5	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.2	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.6	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.4	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.1	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.3	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.4-1.1.4-4.1	$4$	$1$	$C_4$	$4$	$2$	$[ 1; 4, 4 ]$			$(1,2)(3,4),\ldots$
4.4-2.1.2-2-2.1	$4$	$1$	$C_2^2$	$4$	$3$	$[ 1; 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.5-1.0.5-5-5-5.7	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$			$(1,4,2,5,3),\ldots$
4.5-1.0.5-5-5-5.5	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$			$(1,3,5,2,4),\ldots$
4.5-1.0.5-5-5-5.4	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
4.5-1.0.5-5-5-5.2	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
4.5-1.0.5-5-5-5.3	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
4.5-1.0.5-5-5-5.6	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$			$(1,3,5,2,4),\ldots$
4.5-1.0.5-5-5-5.1	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
4.6-2.0.2-6-6-6.1	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.3-3-6-6.2	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 3, 3, 6, 6 ]$			$(1,2,3)(4,5,6),\ldots$
4.6-2.0.2-6-6-6.2	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.3-3-6-6.1	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 3, 3, 6, 6 ]$			$(1,2,3)(4,5,6),\ldots$
4.6-2.0.3-3-6-6.3	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 3, 3, 6, 6 ]$			$(1,3,2)(4,6,5),\ldots$
4.6-2.0.2-2-2-3-6.2	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
4.6-1.0.2-2-3-3-3.1	$4$	$0$	$S_3$	$6$	$2$	$[ 0; 2, 2, 3, 3, 3 ]$		✓	$(1,4)(2,6)(3,5),\ldots$
4.6-2.0.2-2-3-3-3.2	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.2-2-2-3-6.1	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.2-2-3-3-3.1	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
4.6-1.0.2-2-2-2-2-2.1	$4$	$0$	$S_3$	$6$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,6)(3,5),\ldots$
4.6-1.1.2-2.1	$4$	$1$	$S_3$	$6$	$2$	$[ 1; 2, 2 ]$			$(1,2,3)(4,5,6),\ldots$
4.6-2.1.2-2.1	$4$	$1$	$C_6$	$6$	$2$	$[ 1; 2, 2 ]$			$(1,4)(2,5)(3,6),\ldots$
4.8-4.0.2-4-4-4.1	$4$	$0$	$Q_8$	$8$	$1$	$[ 0; 2, 4, 4, 4 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
4.8-1.0.2-2-8-8.1	$4$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 2, 8, 8 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
4.8-1.0.2-2-8-8.2	$4$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 2, 8, 8 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
4.8-3.0.2-2-2-2-4.1	$4$	$0$	$D_4$	$8$	$2$	$[ 0; 2, 2, 2, 2, 4 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
4.8-3.0.2-2-2-2-4.3	$4$	$0$	$D_4$	$8$	$2$	$[ 0; 2, 2, 2, 2, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
4.8-3.0.2-2-2-2-4.2	$4$	$0$	$D_4$	$8$	$2$	$[ 0; 2, 2, 2, 2, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
4.9-1.0.9-9-9.1	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$			$(1,4,7,2,5,8,3,6,9),\ldots$
4.9-1.0.9-9-9.3	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$			$(1,7,5,3,9,4,2,8,6),\ldots$
4.9-1.0.9-9-9.2	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$			$(1,4,7,2,5,8,3,6,9),\ldots$
4.9-1.0.9-9-9.4	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$			$(1,7,5,3,9,4,2,8,6),\ldots$

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Classical	Maass
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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.