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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Results (1-50 of 176 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
3.2-1.0.2-2-2-2-2-2-2-2.1	$3$	$0$	$C_2$	$2$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2),\ldots$
3.3-1.0.3-3-3-3-3.1	$3$	$0$	$C_3$	$3$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
3.3-1.0.3-3-3-3-3.2	$3$	$0$	$C_3$	$3$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
3.4-1.0.4-4-4-4.2	$3$	$0$	$C_4$	$4$	$1$	$[ 0; 4, 4, 4, 4 ]$			$(1,3,2,4),\ldots$
3.4-1.0.4-4-4-4.3	$3$	$0$	$C_4$	$4$	$1$	$[ 0; 4, 4, 4, 4 ]$			$(1,4,2,3),\ldots$
3.4-1.0.4-4-4-4.1	$3$	$0$	$C_4$	$4$	$1$	$[ 0; 4, 4, 4, 4 ]$			$(1,3,2,4),\ldots$
3.4-1.0.2-2-2-4-4.2	$3$	$0$	$C_4$	$4$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
3.4-1.0.2-2-2-4-4.1	$3$	$0$	$C_4$	$4$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.1	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.2	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.7	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,3)(2,4),\ldots$
3.4-2.0.2-2-2-2-2-2.3	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.4	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
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	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
3.6-2.0.2-3-3-6.1	$3$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
3.6-2.0.2-2-6-6.1	$3$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
3.6-2.0.2-3-3-6.2	$3$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
3.6-1.0.2-2-2-2-3.1	$3$	$0$	$S_3$	$6$	$2$	$[ 0; 2, 2, 2, 2, 3 ]$			$(1,4)(2,6)(3,5),\ldots$
3.7-1.0.7-7-7.1	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,2,3,4,5,6,7),\ldots$
3.7-1.0.7-7-7.4	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,3,5,7,2,4,6),\ldots$
3.7-1.0.7-7-7.2	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,2,3,4,5,6,7),\ldots$
3.7-1.0.7-7-7.5	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,3,5,7,2,4,6),\ldots$
3.7-1.0.7-7-7.8	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,5,2,6,3,7,4),\ldots$
3.7-1.0.7-7-7.3	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,2,3,4,5,6,7),\ldots$
3.7-1.0.7-7-7.6	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,4,7,3,6,2,5),\ldots$
3.7-1.0.7-7-7.7	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$			$(1,5,2,6,3,7,4),\ldots$
3.8-1.0.4-8-8.2	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$			$(1,3,2,4)(5,7,6,8),\ldots$
3.8-1.0.4-8-8.1	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$			$(1,3,2,4)(5,7,6,8),\ldots$
3.8-1.0.4-8-8.3	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$			$(1,3,2,4)(5,7,6,8),\ldots$
3.8-1.0.4-8-8.4	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$			$(1,4,2,3)(5,8,6,7),\ldots$
3.8-1.0.4-8-8.6	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$			$(1,4,2,3)(5,8,6,7),\ldots$
3.8-1.0.4-8-8.5	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$			$(1,4,2,3)(5,8,6,7),\ldots$
3.8-3.0.2-2-4-4.1	$3$	$0$	$D_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.5	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.11	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-2.0.2-2-4-4.12	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-2.0.2-2-4-4.4	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.10	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-3.0.2-2-4-4.2	$3$	$0$	$D_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,5)(2,6)(3,8)(4,7),\ldots$
3.8-2.0.2-2-4-4.3	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.2	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.7	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.1	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-2.0.2-2-4-4.8	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.6	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-2.0.2-2-4-4.9	$3$	$0$	$C_2\times C_4$	$8$	$1$	$[ 0; 2, 2, 4, 4 ]$			$(1,3)(2,4)(5,7)(6,8),\ldots$
3.8-5.0.2-2-2-2-2.28	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓		$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-5.0.2-2-2-2-2.26	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓		$(1,4)(2,3)(5,8)(6,7),\ldots$
3.8-5.0.2-2-2-2-2.6	$3$	$0$	$C_2^3$	$8$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$

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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.