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 344 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
2.8-1.0.2-8-8.1	$2$	$0$	$C_8$	$8$	$0$	$[ 0; 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
2.8-1.0.2-8-8.2	$2$	$0$	$C_8$	$8$	$0$	$[ 0; 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
3.8-1.0.4-8-8.3	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
3.8-1.0.4-8-8.5	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$
3.8-1.0.4-8-8.1	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
3.8-1.0.4-8-8.2	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
3.8-1.0.4-8-8.6	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$
3.8-1.0.4-8-8.4	$3$	$0$	$C_8$	$8$	$0$	$[ 0; 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$
4.8-1.0.2-2-8-8.2	$4$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
4.8-1.0.2-2-8-8.1	$4$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 2, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-1.0.2-4-8-8.5	$5$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-1.0.2-4-8-8.1	$5$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-1.0.2-4-8-8.4	$5$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-1.0.2-4-8-8.3	$5$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-1.0.2-4-8-8.6	$5$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-1.0.2-4-8-8.2	$5$	$0$	$C_8$	$8$	$1$	$[ 0; 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
6.8-1.0.4-4-8-8.3	$6$	$0$	$C_8$	$8$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
6.8-1.0.4-4-8-8.6	$6$	$0$	$C_8$	$8$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$
6.8-1.0.4-4-8-8.5	$6$	$0$	$C_8$	$8$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$
6.8-1.0.4-4-8-8.2	$6$	$0$	$C_8$	$8$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
6.8-1.0.4-4-8-8.1	$6$	$0$	$C_8$	$8$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
6.8-1.0.4-4-8-8.4	$6$	$0$	$C_8$	$8$	$1$	$[ 0; 4, 4, 8, 8 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
6.8-1.0.2-2-2-8-8.1	$6$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
6.8-1.0.2-2-2-8-8.2	$6$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 2, 8, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-1.0.8-8-8-8.2	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,5,3,7,2,6,4,8),\ldots$
7.8-1.0.8-8-8-8.4	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,5,3,7,2,6,4,8),\ldots$
7.8-1.0.8-8-8-8.5	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,5,3,7,2,6,4,8),\ldots$
7.8-1.0.8-8-8-8.8	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,7,4,5,2,8,3,6),\ldots$
7.8-1.0.8-8-8-8.9	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,6,3,8,2,5,4,7),\ldots$
7.8-1.0.8-8-8-8.1	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,5,3,7,2,6,4,8),\ldots$
7.8-1.0.8-8-8-8.3	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,5,3,7,2,6,4,8),\ldots$
7.8-1.0.8-8-8-8.6	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,7,4,5,2,8,3,6),\ldots$
7.8-1.0.8-8-8-8.7	$7$	$0$	$C_8$	$8$	$1$	$[ 0; 8, 8, 8, 8 ]$		$(1,7,4,5,2,8,3,6),\ldots$
7.8-1.0.2-2-4-8-8.2	$7$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-1.0.2-2-4-8-8.6	$7$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-1.0.2-2-4-8-8.5	$7$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-1.0.2-2-4-8-8.4	$7$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-1.0.2-2-4-8-8.3	$7$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-1.0.2-2-4-8-8.1	$7$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 2, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-4-4-8-8.3	$8$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-4-4-8-8.2	$8$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-4-4-8-8.4	$8$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-4-4-8-8.1	$8$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-4-4-8-8.5	$8$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-4-4-8-8.6	$8$	$0$	$C_8$	$8$	$2$	$[ 0; 2, 4, 4, 8, 8 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-2-2-2-8-8.2	$8$	$0$	$C_8$	$8$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-1.0.2-2-2-2-8-8.1	$8$	$0$	$C_8$	$8$	$3$	$[ 0; 2, 2, 2, 2, 8, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-1.0.4-4-4-8-8.11	$9$	$0$	$C_8$	$8$	$2$	$[ 0; 4, 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$
9.8-1.0.4-4-4-8-8.12	$9$	$0$	$C_8$	$8$	$2$	$[ 0; 4, 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$
9.8-1.0.4-4-4-8-8.10	$9$	$0$	$C_8$	$8$	$2$	$[ 0; 4, 4, 4, 8, 8 ]$		$(1,4,2,3)(5,8,6,7),\ldots$

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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.