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 (27 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
3.12-3.0.2-2-3-3.1	$3$	$0$	$A_4$	$12$	$1$	$[ 0; 2, 2, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
4.12-3.0.2-3-3-3.1	$4$	$0$	$A_4$	$12$	$1$	$[ 0; 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
4.12-3.0.2-3-3-3.2	$4$	$0$	$A_4$	$12$	$1$	$[ 0; 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
4.12-3.1.2.1	$4$	$1$	$A_4$	$12$	$1$	$[ 1; 2 ]$	$(1,9,5)(2,11,8)(3,12,6)(4,10,7),\ldots$
5.12-3.0.3-3-3-3.1	$5$	$0$	$A_4$	$12$	$1$	$[ 0; 3, 3, 3, 3 ]$	$(1,5,9)(2,8,11)(3,6,12)(4,7,10),\ldots$
6.12-3.0.2-2-2-3-3.1	$6$	$0$	$A_4$	$12$	$2$	$[ 0; 2, 2, 2, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-3.0.2-2-3-3-3.2	$7$	$0$	$A_4$	$12$	$2$	$[ 0; 2, 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-3.0.2-2-3-3-3.1	$7$	$0$	$A_4$	$12$	$2$	$[ 0; 2, 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
8.12-3.0.2-3-3-3-3.1	$8$	$0$	$A_4$	$12$	$2$	$[ 0; 2, 3, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
9.12-3.0.3-3-3-3-3.2	$9$	$0$	$A_4$	$12$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	$(1,5,9)(2,8,11)(3,6,12)(4,7,10),\ldots$
9.12-3.0.3-3-3-3-3.1	$9$	$0$	$A_4$	$12$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	$(1,5,9)(2,8,11)(3,6,12)(4,7,10),\ldots$
9.12-3.0.2-2-2-2-3-3.1	$9$	$0$	$A_4$	$12$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
10.12-3.0.2-2-2-3-3-3.2	$10$	$0$	$A_4$	$12$	$3$	$[ 0; 2, 2, 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
10.12-3.0.2-2-2-3-3-3.1	$10$	$0$	$A_4$	$12$	$3$	$[ 0; 2, 2, 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
11.12-3.0.2-2-3-3-3-3.1	$11$	$0$	$A_4$	$12$	$3$	$[ 0; 2, 2, 3, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-3.0.2-3-3-3-3-3.2	$12$	$0$	$A_4$	$12$	$3$	$[ 0; 2, 3, 3, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-3.0.2-3-3-3-3-3.1	$12$	$0$	$A_4$	$12$	$3$	$[ 0; 2, 3, 3, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
12.12-3.0.2-2-2-2-2-3-3.1	$12$	$0$	$A_4$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
13.12-3.0.3-3-3-3-3-3.2	$13$	$0$	$A_4$	$12$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	$(1,5,9)(2,8,11)(3,6,12)(4,7,10),\ldots$
13.12-3.0.3-3-3-3-3-3.3	$13$	$0$	$A_4$	$12$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	$(1,9,5)(2,11,8)(3,12,6)(4,10,7),\ldots$
13.12-3.0.3-3-3-3-3-3.1	$13$	$0$	$A_4$	$12$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	$(1,5,9)(2,8,11)(3,6,12)(4,7,10),\ldots$
13.12-3.0.2-2-2-2-3-3-3.1	$13$	$0$	$A_4$	$12$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
13.12-3.0.2-2-2-2-3-3-3.2	$13$	$0$	$A_4$	$12$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
14.12-3.0.2-2-2-3-3-3-3.1	$14$	$0$	$A_4$	$12$	$4$	$[ 0; 2, 2, 2, 3, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
15.12-3.0.2-2-3-3-3-3-3.2	$15$	$0$	$A_4$	$12$	$4$	$[ 0; 2, 2, 3, 3, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
15.12-3.0.2-2-3-3-3-3-3.1	$15$	$0$	$A_4$	$12$	$4$	$[ 0; 2, 2, 3, 3, 3, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
15.12-3.0.2-2-2-2-2-2-3-3.1	$15$	$0$	$A_4$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 3, 3 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$

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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.