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 (22 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
13.12-4.0.2-2-3-3-6-6.1	$13$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 3, 3, 6, 6 ]$	$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
13.12-4.0.2-2-3-3-6-6.2	$13$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 3, 3, 6, 6 ]$	$(1,10)(2,12)(3,11)(4,7)(5,9)(6,8),\ldots$
13.12-4.0.2-2-2-6-6-6.2	$13$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 6, 6, 6 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-6-6-6.1	$13$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 6, 6, 6 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-3-3-3.1	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-3-3-3.2	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-3-3-3.3	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$	$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
13.12-4.0.2-2-2-2-2-3-6.1	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-3-6.2	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-3-6.3	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-3-6.4	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-3-6.5	$13$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.1	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.2	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.3	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.4	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.5	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.6	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.7	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.8	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.9	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
13.12-4.0.2-2-2-2-2-2-2-2.10	$13$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$

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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.