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 1421 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
14.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$14$	$0$	$C_2$	$2$	$27$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.2	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.3	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.4	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.1	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.5	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.1	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.5	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.4	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.3	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.2	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-4-4-4-4-4-4-4-4.2	$14$	$0$	$C_4$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-4-4-4-4-4-4-4-4.3	$14$	$0$	$C_4$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-4-4-4-4-4-4-4-4.1	$14$	$0$	$C_4$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-4-4-4-4-4-4-4-4.4	$14$	$0$	$C_4$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-2-2-2-4-4-4-4-4-4.1	$14$	$0$	$C_4$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-2-2-2-4-4-4-4-4-4.2	$14$	$0$	$C_4$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-2-2-2-4-4-4-4-4-4.3	$14$	$0$	$C_4$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-2-2-2-2-2-2-4-4-4-4.2	$14$	$0$	$C_4$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-2-2-2-2-2-2-4-4-4-4.1	$14$	$0$	$C_4$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4),\ldots$
14.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.1	$14$	$0$	$C_4$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.9	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.8	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.7	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.6	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.5	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.24	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.25	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.4	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.10	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.30	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.31	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.3	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.2	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.19	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.18	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.17	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.28	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.16	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.14	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.20	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.15	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.21	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.22	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.23	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.26	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.13	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.12	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.11	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$

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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.