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 at least 1000)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
10.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$10$	$0$	$C_2$	$2$	$19$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.3	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.1	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.2	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.4	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.5	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,3,2),\ldots$
10.4-1.0.2-4-4-4-4-4-4-4-4.1	$10$	$0$	$C_4$	$4$	$6$	$[ 0; 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-4-4-4-4-4-4-4-4.3	$10$	$0$	$C_4$	$4$	$6$	$[ 0; 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-4-4-4-4-4-4-4-4.2	$10$	$0$	$C_4$	$4$	$6$	$[ 0; 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-4-4-4-4-4-4-4-4.4	$10$	$0$	$C_4$	$4$	$6$	$[ 0; 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-2-2-2-4-4-4-4-4-4.3	$10$	$0$	$C_4$	$4$	$7$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-2-2-2-4-4-4-4-4-4.1	$10$	$0$	$C_4$	$4$	$7$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-2-2-2-4-4-4-4-4-4.2	$10$	$0$	$C_4$	$4$	$7$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-2-2-2-2-2-2-4-4-4-4.2	$10$	$0$	$C_4$	$4$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-2-2-2-2-2-2-4-4-4-4.1	$10$	$0$	$C_4$	$4$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
10.4-1.0.2-2-2-2-2-2-2-2-2-2-4-4.1	$10$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.6	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.5	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.10	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.15	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.8	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.3	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.13	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.19	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.11	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.14	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.4	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.9	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.1	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.17	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.20	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.16	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.21	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.2	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.18	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.12	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2.7	$10$	$0$	$C_2^2$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.11	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.22	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.1	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.10	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.24	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,4,2,5,3),\ldots$
10.5-1.0.5-5-5-5-5-5-5.18	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.6	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.17	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.8	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.14	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.3	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.13	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.7	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$			$(1,2,3,4,5),\ldots$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
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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.