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 133 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
2.12-4.0.2-2-2-3.1	$2$	$0$	$D_6$	$12$	$1$	$[ 0; 2, 2, 2, 3 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
3.12-4.0.2-2-2-6.2	$3$	$0$	$D_6$	$12$	$1$	$[ 0; 2, 2, 2, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
3.12-4.0.2-2-2-6.1	$3$	$0$	$D_6$	$12$	$1$	$[ 0; 2, 2, 2, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-4.0.2-2-3-6.1	$4$	$0$	$D_6$	$12$	$1$	$[ 0; 2, 2, 3, 6 ]$		✓	$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
4.12-4.0.2-2-2-2-2.1	$4$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-4.0.2-2-2-2-2.2	$4$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-4.0.2-2-6-6.2	$5$	$0$	$D_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$			$(1,10)(2,12)(3,11)(4,7)(5,9)(6,8),\ldots$
5.12-4.0.2-2-6-6.1	$5$	$0$	$D_6$	$12$	$1$	$[ 0; 2, 2, 6, 6 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
5.12-4.0.2-2-2-2-3.2	$5$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 3 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-4.0.2-2-2-2-3.3	$5$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 3 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
5.12-4.0.2-2-2-2-3.1	$5$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 3 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-4.0.2-2-2-3-3.1	$6$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 3 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-4.0.2-2-2-2-6.3	$6$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 6 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
6.12-4.0.2-2-2-2-6.1	$6$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-4.0.2-2-2-2-6.2	$6$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 6 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
7.12-4.0.2-2-2-3-6.2	$7$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-4.0.2-2-2-3-6.1	$7$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-4.0.2-2-2-2-2-2.1	$7$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-4.0.2-2-2-2-2-2.5	$7$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
7.12-4.0.2-2-2-2-2-2.4	$7$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
7.12-4.0.2-2-2-2-2-2.3	$7$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-4.0.2-2-2-2-2-2.2	$7$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-4.0.2-2-2-6-6.1	$8$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-4.0.2-2-3-3-6.1	$8$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 3, 3, 6 ]$		✓	$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
8.12-4.0.2-2-2-2-2-3.1	$8$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 3 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-4.0.2-2-2-2-2-3.3	$8$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 3 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
8.12-4.0.2-2-2-2-2-3.2	$8$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 3 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-4.0.2-2-3-6-6.2	$9$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 3, 6, 6 ]$			$(1,10)(2,12)(3,11)(4,7)(5,9)(6,8),\ldots$
9.12-4.0.2-2-3-6-6.1	$9$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 3, 6, 6 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
9.12-4.0.2-2-2-2-2-6.5	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-4.0.2-2-2-2-2-6.4	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-4.0.2-2-2-2-2-6.3	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-4.0.2-2-2-2-3-3.3	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
9.12-4.0.2-2-2-2-3-3.2	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-4.0.2-2-2-2-3-3.1	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-4.0.2-2-2-2-2-6.2	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-4.0.2-2-2-2-2-6.1	$9$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 2, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-4.0.2-2-6-6-6.1	$10$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 6, 6, 6 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
10.12-4.0.2-2-2-2-3-6.1	$10$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 3, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-4.0.2-2-2-3-3-3.1	$10$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-4.0.2-2-2-2-3-6.3	$10$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 3, 6 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
10.12-4.0.2-2-2-2-3-6.2	$10$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 3, 6 ]$			$(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
10.12-4.0.2-2-2-2-2-2-2.4	$10$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-4.0.2-2-2-2-2-2-2.3	$10$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-4.0.2-2-2-2-2-2-2.2	$10$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-4.0.2-2-2-2-2-2-2.1	$10$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-4.0.2-2-2-2-2-2-2.5	$10$	$0$	$D_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-4.0.2-2-2-2-6-6.5	$11$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 6, 6 ]$			$(1,10)(2,12)(3,11)(4,7)(5,9)(6,8),\ldots$
11.12-4.0.2-2-2-3-3-6.2	$11$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 3, 3, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-4.0.2-2-2-3-3-6.1	$11$	$0$	$D_6$	$12$	$3$	$[ 0; 2, 2, 2, 3, 3, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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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.