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 (1-50 of 752 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Cyclic trigonal	Generating vectors
2.12-5.0.2-6-6.1	$2$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
2.12-5.0.2-6-6.5	$2$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 2, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
2.12-5.0.2-6-6.2	$2$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
2.12-5.0.2-6-6.3	$2$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 2, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
2.12-5.0.2-6-6.6	$2$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 2, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
2.12-5.0.2-6-6.4	$2$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 2, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
4.12-5.0.6-6-6.2	$4$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 6, 6, 6 ]$		$(1,6,2,4,3,5)(7,12,8,10,9,11),\ldots$
4.12-5.0.6-6-6.1	$4$	$0$	$C_2\times C_6$	$12$	$0$	$[ 0; 6, 6, 6 ]$		$(1,5,3,4,2,6)(7,11,9,10,8,12),\ldots$
4.12-5.0.2-2-3-6.2	$4$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 3, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-5.0.2-2-3-6.6	$4$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 3, 6 ]$	✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
4.12-5.0.2-2-3-6.5	$4$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 3, 6 ]$	✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
4.12-5.0.2-2-3-6.1	$4$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 3, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-5.0.2-2-3-6.4	$4$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 3, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-5.0.2-2-3-6.3	$4$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 3, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-5.0.2-2-6-6.12	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
5.12-5.0.2-2-6-6.9	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
5.12-5.0.2-2-6-6.3	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-5.0.2-2-6-6.2	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-5.0.2-2-6-6.1	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-5.0.2-2-6-6.11	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
5.12-5.0.2-2-6-6.5	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-5.0.2-2-6-6.7	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
5.12-5.0.2-2-6-6.8	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
5.12-5.0.2-2-6-6.10	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
5.12-5.0.2-2-6-6.4	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-5.0.2-2-6-6.6	$5$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-5.0.2-3-6-6.2	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-5.0.2-3-6-6.1	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-5.0.2-3-6-6.6	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$	✓	$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
6.12-5.0.2-3-6-6.5	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$	✓	$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
6.12-5.0.2-3-6-6.4	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$	✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
6.12-5.0.2-3-6-6.3	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$	✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
6.12-5.0.2-2-2-3-3.1	$6$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 3 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-6-6-6.12	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
7.12-5.0.2-6-6-6.10	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
7.12-5.0.2-6-6-6.11	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
7.12-5.0.2-6-6-6.5	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
7.12-5.0.2-6-6-6.9	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
7.12-5.0.2-6-6-6.7	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
7.12-5.0.2-6-6-6.6	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
7.12-5.0.2-6-6-6.2	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-6-6-6.1	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-6-6-6.8	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
7.12-5.0.2-6-6-6.3	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-6-6-6.4	$7$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 6, 6, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-2-2-3-6.2	$7$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-2-2-3-6.12	$7$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$		$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
7.12-5.0.2-2-2-3-6.4	$7$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-2-2-3-6.1	$7$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-5.0.2-2-2-3-6.3	$7$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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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.