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 (33 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
8.12-5.0.3-6-6-6.1	$8$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 3, 6, 6, 6 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
8.12-5.0.3-6-6-6.2	$8$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 3, 6, 6, 6 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
8.12-5.0.3-6-6-6.4	$8$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 3, 6, 6, 6 ]$		✓	$(1,3,2)(4,6,5)(7,9,8)(10,12,11),\ldots$
8.12-5.0.3-6-6-6.6	$8$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 3, 6, 6, 6 ]$		✓	$(1,3,2)(4,6,5)(7,9,8)(10,12,11),\ldots$
8.12-5.0.3-6-6-6.5	$8$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 3, 6, 6, 6 ]$		✓	$(1,3,2)(4,6,5)(7,9,8)(10,12,11),\ldots$
8.12-5.0.3-6-6-6.3	$8$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 3, 6, 6, 6 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
8.12-5.0.2-2-3-3-6.3	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-3-3-6.4	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-3-3-6.5	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 3, 3, 6 ]$		✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-3-3-6.6	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 3, 3, 6 ]$		✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-2-6-6.1	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.2	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.10	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.15	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$	✓		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-2-6-6.20	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$	✓		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
8.12-5.0.2-2-2-6-6.21	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$	✓		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
8.12-5.0.2-2-2-6-6.13	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.12	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.17	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-2-6-6.3	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.16	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-2-6-6.18	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-2-6-6.19	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-2-6-6.7	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.6	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.5	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.4	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.14	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$	✓		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
8.12-5.0.2-2-2-6-6.11	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.9	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-2-6-6.8	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-3-3-6.1	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-5.0.2-2-3-3-6.2	$8$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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Overview	Random
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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.