LMFDB - Family of higher genus curves with automorphisms search results

The results below are complete, since the LMFDB contains all groups G acting as automorphisms of curves X with the genus of X at most 15 and the genus of X/G equal to 0

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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 409 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
6.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$6$	$0$	$C_2$	$2$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.3	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.2	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.1	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
6.4-1.0.4-4-4-4-4-4.1	$6$	$0$	$C_4$	$4$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$			$(1,3,2,4),\ldots$
6.4-1.0.4-4-4-4-4-4.2	$6$	$0$	$C_4$	$4$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$			$(1,3,2,4),\ldots$
6.4-1.0.4-4-4-4-4-4.3	$6$	$0$	$C_4$	$4$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$			$(1,3,2,4),\ldots$
6.4-1.0.2-2-2-4-4-4-4.2	$6$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
6.4-1.0.2-2-2-4-4-4-4.1	$6$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
6.4-1.0.2-2-2-2-2-2-4-4.1	$6$	$0$	$C_4$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.1	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.3	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.4	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.6	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.8	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.9	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.10	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.7	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.2	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.5	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
6.5-1.0.5-5-5-5-5.12	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,5,4,3,2),\ldots$
6.5-1.0.5-5-5-5-5.4	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.3	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.2	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.11	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,4,2,5,3),\ldots$
6.5-1.0.5-5-5-5-5.5	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.1	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.10	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,3,5,2,4),\ldots$
6.5-1.0.5-5-5-5-5.9	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,3,5,2,4),\ldots$
6.5-1.0.5-5-5-5-5.8	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,3,5,2,4),\ldots$
6.5-1.0.5-5-5-5-5.7	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.6	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
6.6-2.0.3-3-3-6-6.4	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,3,2)(4,6,5),\ldots$
6.6-2.0.2-3-6-6-6.1	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 3, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.3-3-3-6-6.2	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-2.0.2-3-6-6-6.2	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 3, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.3-3-3-6-6.3	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-2.0.3-3-3-6-6.1	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-1.0.2-2-3-3-3-3.1	$6$	$0$	$S_3$	$6$	$3$	$[ 0; 2, 2, 3, 3, 3, 3 ]$		✓	$(1,4)(2,6)(3,5),\ldots$
6.6-2.0.2-2-3-3-3-3.1	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 3, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-2-2-3-3-6.1	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 3, 3, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-2-2-2-6-6.1	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 2, 6, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-2-2-3-3-6.2	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 3, 3, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-1.0.2-2-2-2-2-2-3.1	$6$	$0$	$S_3$	$6$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 3 ]$			$(1,4)(2,6)(3,5),\ldots$
6.7-1.0.7-7-7-7.2	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$			$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.6	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$			$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.5	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$			$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.16	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$			$(1,4,7,3,6,2,5),\ldots$
6.7-1.0.7-7-7-7.14	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$			$(1,4,7,3,6,2,5),\ldots$
6.7-1.0.7-7-7-7.13	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$			$(1,3,5,7,2,4,6),\ldots$

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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 $\F_{q}$
Belyi maps

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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.