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 411 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Cyclic trigonal	Generating vectors
3.12-2.0.3-4-12.2	$3$	$0$	$C_{12}$	$12$	$0$	$[ 0; 3, 4, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
3.12-2.0.3-4-12.1	$3$	$0$	$C_{12}$	$12$	$0$	$[ 0; 3, 4, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
3.12-2.0.2-12-12.1	$3$	$0$	$C_{12}$	$12$	$0$	$[ 0; 2, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
3.12-2.0.3-4-12.3	$3$	$0$	$C_{12}$	$12$	$0$	$[ 0; 3, 4, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
3.12-2.0.3-4-12.4	$3$	$0$	$C_{12}$	$12$	$0$	$[ 0; 3, 4, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
3.12-2.0.2-12-12.2	$3$	$0$	$C_{12}$	$12$	$0$	$[ 0; 2, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
4.12-2.0.4-6-12.3	$4$	$0$	$C_{12}$	$12$	$0$	$[ 0; 4, 6, 12 ]$		$(1,8,2,7)(3,10,4,9)(5,12,6,11),\ldots$
4.12-2.0.4-6-12.4	$4$	$0$	$C_{12}$	$12$	$0$	$[ 0; 4, 6, 12 ]$		$(1,8,2,7)(3,10,4,9)(5,12,6,11),\ldots$
4.12-2.0.4-6-12.1	$4$	$0$	$C_{12}$	$12$	$0$	$[ 0; 4, 6, 12 ]$		$(1,7,2,8)(3,9,4,10)(5,11,6,12),\ldots$
4.12-2.0.4-6-12.2	$4$	$0$	$C_{12}$	$12$	$0$	$[ 0; 4, 6, 12 ]$		$(1,7,2,8)(3,9,4,10)(5,11,6,12),\ldots$
4.12-2.0.3-12-12.2	$4$	$0$	$C_{12}$	$12$	$0$	$[ 0; 3, 12, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
4.12-2.0.3-12-12.1	$4$	$0$	$C_{12}$	$12$	$0$	$[ 0; 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
5.12-2.0.6-12-12.2	$5$	$0$	$C_{12}$	$12$	$0$	$[ 0; 6, 12, 12 ]$		$(1,4,5,2,3,6)(7,10,11,8,9,12),\ldots$
5.12-2.0.6-12-12.3	$5$	$0$	$C_{12}$	$12$	$0$	$[ 0; 6, 12, 12 ]$		$(1,6,3,2,5,4)(7,12,9,8,11,10),\ldots$
5.12-2.0.6-12-12.1	$5$	$0$	$C_{12}$	$12$	$0$	$[ 0; 6, 12, 12 ]$		$(1,4,5,2,3,6)(7,10,11,8,9,12),\ldots$
5.12-2.0.6-12-12.4	$5$	$0$	$C_{12}$	$12$	$0$	$[ 0; 6, 12, 12 ]$		$(1,6,3,2,5,4)(7,12,9,8,11,10),\ldots$
6.12-2.0.2-3-4-12.3	$6$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
6.12-2.0.2-3-4-12.4	$6$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
6.12-2.0.2-3-4-12.1	$6$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
6.12-2.0.2-2-12-12.2	$6$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 2, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
6.12-2.0.2-2-12-12.1	$6$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 2, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
6.12-2.0.2-3-4-12.2	$6$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 4, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
6.12-2.0.3-3-4-4.1	$6$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 4, 4 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
7.12-2.0.3-4-4-6.2	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 4, 6 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
7.12-2.0.2-4-6-12.4	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 4, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.2-3-12-12.3	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.2-3-12-12.2	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.2-3-12-12.1	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.3-3-4-12.2	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 4, 12 ]$	✓	$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
7.12-2.0.3-3-4-12.4	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 4, 12 ]$	✓	$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
7.12-2.0.2-4-6-12.2	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 4, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.3-3-4-12.1	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 4, 12 ]$	✓	$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
7.12-2.0.2-4-6-12.3	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 4, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.2-4-6-12.1	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 4, 6, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.3-3-4-12.3	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 4, 12 ]$	✓	$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
7.12-2.0.3-4-4-6.1	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 4, 6 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
7.12-2.0.3-4-4-6.3	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 4, 6 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
7.12-2.0.2-3-12-12.4	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 3, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
7.12-2.0.3-4-4-6.4	$7$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 4, 6 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
8.12-2.0.3-4-6-12.3	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 6, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
8.12-2.0.3-4-6-12.2	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
8.12-2.0.3-4-6-12.4	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 6, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
8.12-2.0.3-4-6-12.1	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 4, 6, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
8.12-2.0.3-3-12-12.4	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 12, 12 ]$		$(1,5,3)(2,6,4)(7,11,9)(8,12,10),\ldots$
8.12-2.0.3-3-12-12.3	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
8.12-2.0.3-3-12-12.2	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
8.12-2.0.3-3-12-12.1	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 3, 3, 12, 12 ]$		$(1,3,5)(2,4,6)(7,9,11)(8,10,12),\ldots$
8.12-2.0.4-4-6-6.1	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 4, 4, 6, 6 ]$		$(1,7,2,8)(3,9,4,10)(5,11,6,12),\ldots$
8.12-2.0.2-6-12-12.2	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$
8.12-2.0.2-6-12-12.1	$8$	$0$	$C_{12}$	$12$	$1$	$[ 0; 2, 6, 12, 12 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12),\ldots$

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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.