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 65 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
2.12-1.0.3-4-4.1	$2$	$0$	$C_3:C_4$	$12$	$0$	$[ 0; 3, 4, 4 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
3.12-1.0.4-4-6.2	$3$	$0$	$C_3:C_4$	$12$	$0$	$[ 0; 4, 4, 6 ]$			$(1,10,4,7)(2,12,5,9)(3,11,6,8),\ldots$
3.12-1.0.4-4-6.1	$3$	$0$	$C_3:C_4$	$12$	$0$	$[ 0; 4, 4, 6 ]$			$(1,7,4,10)(2,9,5,12)(3,8,6,11),\ldots$
5.12-1.0.2-3-4-4.2	$5$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 2, 3, 4, 4 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-1.0.2-3-4-4.1	$5$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 2, 3, 4, 4 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-1.0.3-3-4-4.1	$6$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 3, 3, 4, 4 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
6.12-1.0.2-4-4-6.1	$6$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 2, 4, 4, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
7.12-1.0.3-4-4-6.1	$7$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 3, 4, 4, 6 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
7.12-1.0.4-4-4-4.3	$7$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 4, 4, 4, 4 ]$			$(1,10,4,7)(2,12,5,9)(3,11,6,8),\ldots$
7.12-1.0.3-4-4-6.2	$7$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 3, 4, 4, 6 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
7.12-1.0.4-4-4-4.1	$7$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 4, 4, 4, 4 ]$			$(1,7,4,10)(2,9,5,12)(3,8,6,11),\ldots$
7.12-1.0.4-4-4-4.2	$7$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 4, 4, 4, 4 ]$			$(1,7,4,10)(2,9,5,12)(3,8,6,11),\ldots$
8.12-1.0.4-4-6-6.1	$8$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 4, 4, 6, 6 ]$			$(1,7,4,10)(2,9,5,12)(3,8,6,11),\ldots$
8.12-1.0.2-2-3-4-4.1	$8$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-1.0.2-2-4-4-6.1	$9$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 2, 4, 4, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-1.0.2-2-4-4-6.2	$9$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 2, 4, 4, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-1.0.2-3-3-4-4.2	$9$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 3, 3, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-1.0.2-3-3-4-4.1	$9$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 3, 3, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-1.0.2-4-4-4-4.1	$10$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-1.0.2-3-4-4-6.1	$10$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 3, 4, 4, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-1.0.2-4-4-4-4.2	$10$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
10.12-1.0.3-3-3-4-4.1	$10$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 3, 3, 3, 4, 4 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
11.12-1.0.3-4-4-4-4.3	$11$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 3, 4, 4, 4, 4 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
11.12-1.0.3-3-4-4-6.1	$11$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 3, 3, 4, 4, 6 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
11.12-1.0.3-3-4-4-6.2	$11$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 3, 3, 4, 4, 6 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
11.12-1.0.2-4-4-6-6.1	$11$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 4, 4, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-1.0.2-4-4-6-6.2	$11$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 4, 4, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-1.0.3-4-4-4-4.1	$11$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 3, 4, 4, 4, 4 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
11.12-1.0.3-4-4-4-4.2	$11$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 3, 4, 4, 4, 4 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
11.12-1.0.2-2-2-3-4-4.1	$11$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 4 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-1.0.2-2-2-3-4-4.2	$11$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 4 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
12.12-1.0.3-4-4-6-6.1	$12$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 3, 4, 4, 6, 6 ]$			$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
12.12-1.0.4-4-4-4-6.2	$12$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 4, 4, 4, 4, 6 ]$			$(1,7,4,10)(2,9,5,12)(3,8,6,11),\ldots$
12.12-1.0.4-4-4-4-6.1	$12$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 4, 4, 4, 4, 6 ]$			$(1,7,4,10)(2,9,5,12)(3,8,6,11),\ldots$
12.12-1.0.2-2-3-3-4-4.1	$12$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 3, 3, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
12.12-1.0.2-2-2-4-4-6.1	$12$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 2, 4, 4, 6 ]$	✓		$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-1.0.4-4-6-6-6.1	$13$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 4, 4, 6, 6, 6 ]$			$(1,7,4,10)(2,9,5,12)(3,8,6,11),\ldots$
13.12-1.0.4-4-6-6-6.2	$13$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 4, 4, 6, 6, 6 ]$			$(1,10,4,7)(2,12,5,9)(3,11,6,8),\ldots$
13.12-1.0.2-2-4-4-4-4.3	$13$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-1.0.2-2-3-4-4-6.1	$13$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 3, 4, 4, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-1.0.2-2-3-4-4-6.2	$13$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 3, 4, 4, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-1.0.2-3-3-3-4-4.2	$13$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 3, 3, 3, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-1.0.2-3-3-3-4-4.1	$13$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 3, 3, 3, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-1.0.2-2-4-4-4-4.1	$13$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
13.12-1.0.2-2-4-4-4-4.2	$13$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.12-1.0.2-3-3-4-4-6.1	$14$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 3, 3, 4, 4, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.12-1.0.3-3-3-3-4-4.1	$14$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 3, 3, 3, 3, 4, 4 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12),\ldots$
14.12-1.0.2-3-4-4-4-4.1	$14$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 3, 4, 4, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.12-1.0.2-3-4-4-4-4.2	$14$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 3, 4, 4, 4, 4 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.12-1.0.2-2-4-4-6-6.1	$14$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 4, 4, 6, 6 ]$			$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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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.