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 196 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Cyclic trigonal	Generating vectors
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.3	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.4	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.5	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.2	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.1	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.6-2.0.3-3-3-3-3-6-6.5	$10$	$0$	$C_6$	$6$	$4$	$[ 0; 3, 3, 3, 3, 3, 6, 6 ]$	✓	$(1,2,3)(4,5,6),\ldots$
10.6-2.0.3-3-3-3-3-6-6.6	$10$	$0$	$C_6$	$6$	$4$	$[ 0; 3, 3, 3, 3, 3, 6, 6 ]$	✓	$(1,3,2)(4,6,5),\ldots$
10.6-2.0.3-3-3-3-3-6-6.4	$10$	$0$	$C_6$	$6$	$4$	$[ 0; 3, 3, 3, 3, 3, 6, 6 ]$	✓	$(1,2,3)(4,5,6),\ldots$
10.6-2.0.3-3-3-3-3-6-6.2	$10$	$0$	$C_6$	$6$	$4$	$[ 0; 3, 3, 3, 3, 3, 6, 6 ]$	✓	$(1,2,3)(4,5,6),\ldots$
10.6-2.0.3-3-3-3-3-6-6.1	$10$	$0$	$C_6$	$6$	$4$	$[ 0; 3, 3, 3, 3, 3, 6, 6 ]$	✓	$(1,2,3)(4,5,6),\ldots$
10.6-2.0.3-3-3-3-3-6-6.3	$10$	$0$	$C_6$	$6$	$4$	$[ 0; 3, 3, 3, 3, 3, 6, 6 ]$	✓	$(1,2,3)(4,5,6),\ldots$
10.6-2.0.2-2-3-3-3-3-3-3.3	$10$	$0$	$C_6$	$6$	$5$	$[ 0; 2, 2, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
10.6-2.0.2-2-3-3-3-3-3-3.2	$10$	$0$	$C_6$	$6$	$5$	$[ 0; 2, 2, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
10.6-1.0.2-2-3-3-3-3-3-3.1	$10$	$0$	$S_3$	$6$	$5$	$[ 0; 2, 2, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4)(2,6)(3,5),\ldots$
10.6-2.0.2-2-3-3-3-3-3-3.1	$10$	$0$	$C_6$	$6$	$5$	$[ 0; 2, 2, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
10.9-2.0.3-3-3-3-3-3.72	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.177	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,7,4)(2,8,5)(3,9,6),\ldots$
10.9-2.0.3-3-3-3-3-3.6	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.146	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
10.9-2.0.3-3-3-3-3-3.67	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.63	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.37	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.173	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,7,4)(2,8,5)(3,9,6),\ldots$
10.9-2.0.3-3-3-3-3-3.3	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.161	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
10.9-2.0.3-3-3-3-3-3.89	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
10.9-2.0.3-3-3-3-3-3.88	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
10.9-2.0.3-3-3-3-3-3.57	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.85	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.125	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
10.9-2.0.3-3-3-3-3-3.1	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.87	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
10.9-2.0.3-3-3-3-3-3.124	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
10.9-2.0.3-3-3-3-3-3.129	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
10.9-2.0.3-3-3-3-3-3.130	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
10.9-2.0.3-3-3-3-3-3.5	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.162	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
10.9-2.0.3-3-3-3-3-3.178	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,7,4)(2,8,5)(3,9,6),\ldots$
10.9-2.0.3-3-3-3-3-3.54	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.56	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.141	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
10.9-2.0.3-3-3-3-3-3.84	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.4	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.163	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
10.9-2.0.3-3-3-3-3-3.176	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,7,4)(2,8,5)(3,9,6),\ldots$
10.9-2.0.3-3-3-3-3-3.140	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
10.9-2.0.3-3-3-3-3-3.2	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.80	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
10.9-2.0.3-3-3-3-3-3.147	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
10.9-2.0.3-3-3-3-3-3.38	$10$	$0$	$C_3^2$	$9$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$

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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.