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

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Results (47 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
12.12-2.0.2-4-4-12-12.6	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 4, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.3-3-3-12-12.5	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 3, 12, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-3-3-12-12.6	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 3, 12, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-3-3-12-12.1	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-3-3-12-12.2	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-3-3-12-12.3	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.2-3-6-12-12.4	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 3, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-3-6-12-12.6	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 3, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-3-6-12-12.1	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 3, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-4-4-12-12.1	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 4, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-4-4-12-12.3	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 4, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-4-4-12-12.2	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 4, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.3-3-3-12-12.4	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.2-4-4-12-12.5	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 4, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-4-4-12-12.4	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 4, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.3-3-4-6-12.5	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-3-4-6-12.6	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-3-4-6-12.2	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.2-4-6-6-12.3	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 6, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-4-6-6-12.4	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 6, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.3-3-4-6-12.3	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-3-4-6-12.8	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-3-4-6-12.7	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-3-4-6-12.1	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.2-4-6-6-12.1	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 6, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-4-6-6-12.2	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 4, 6, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.3-3-4-6-12.4	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-4-4-4-12.1	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-4-4-4-12.2	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-4-4-4-12.3	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-4-4-4-12.5	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-4-4-4-12.4	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.3-4-4-4-12.8	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-4-4-4-12.7	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-4-4-4-12.6	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 4, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-4-4-6-6.2	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 6, 6 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
12.12-2.0.3-4-4-6-6.1	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 3, 4, 4, 6, 6 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
12.12-2.0.2-3-6-12-12.5	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 3, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-3-6-12-12.3	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 3, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-3-6-12-12.2	$12$	$0$	$C_{12}$	$12$	$2$	$[ 0; 2, 3, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-2-3-3-4-4.1	$12$	$0$	$C_{12}$	$12$	$3$	$[ 0; 2, 2, 3, 3, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-2-2-3-4-12.1	$12$	$0$	$C_{12}$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-2-2-3-4-12.2	$12$	$0$	$C_{12}$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-2-2-3-4-12.3	$12$	$0$	$C_{12}$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-2-2-3-4-12.4	$12$	$0$	$C_{12}$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-2-2-2-12-12.1	$12$	$0$	$C_{12}$	$12$	$3$	$[ 0; 2, 2, 2, 2, 12, 12 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-2.0.2-2-2-2-12-12.2	$12$	$0$	$C_{12}$	$12$	$3$	$[ 0; 2, 2, 2, 2, 12, 12 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$

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Overview	Random
Universe	Knowledge

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.