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 288 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Cyclic trigonal	Generating vectors
3.9-1.0.3-9-9.2	$3$	$0$	$C_9$	$9$	$0$	$[ 0; 3, 9, 9 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
3.9-1.0.3-9-9.1	$3$	$0$	$C_9$	$9$	$0$	$[ 0; 3, 9, 9 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
3.9-1.0.3-9-9.6	$3$	$0$	$C_9$	$9$	$0$	$[ 0; 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
3.9-1.0.3-9-9.4	$3$	$0$	$C_9$	$9$	$0$	$[ 0; 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
3.9-1.0.3-9-9.5	$3$	$0$	$C_9$	$9$	$0$	$[ 0; 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
3.9-1.0.3-9-9.3	$3$	$0$	$C_9$	$9$	$0$	$[ 0; 3, 9, 9 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
4.9-1.0.9-9-9.1	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
4.9-1.0.9-9-9.6	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$		$(1,8,4,3,7,6,2,9,5),\ldots$
4.9-1.0.9-9-9.2	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
4.9-1.0.9-9-9.4	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$		$(1,7,5,3,9,4,2,8,6),\ldots$
4.9-1.0.9-9-9.3	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$		$(1,7,5,3,9,4,2,8,6),\ldots$
4.9-1.0.9-9-9.5	$4$	$0$	$C_9$	$9$	$0$	$[ 0; 9, 9, 9 ]$		$(1,5,9,2,6,7,3,4,8),\ldots$
6.9-1.0.3-3-9-9.1	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.8	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
6.9-1.0.3-3-9-9.7	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
6.9-1.0.3-3-9-9.2	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.3	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.6	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.5	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.4	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.9	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.14	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.12	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.1	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-1.0.3-9-9-9.2	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-1.0.3-9-9-9.11	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.10	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.13	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.8	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.9	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-1.0.3-9-9-9.6	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-1.0.3-9-9-9.3	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-1.0.3-9-9-9.4	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-1.0.3-9-9-9.5	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-1.0.3-9-9-9.7	$7$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 9, 9, 9 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
8.9-1.0.9-9-9-9.7	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,7,5,3,9,4,2,8,6),\ldots$
8.9-1.0.9-9-9-9.12	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,8,4,3,7,6,2,9,5),\ldots$
8.9-1.0.9-9-9-9.2	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
8.9-1.0.9-9-9-9.6	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
8.9-1.0.9-9-9-9.8	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,7,5,3,9,4,2,8,6),\ldots$
8.9-1.0.9-9-9-9.3	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
8.9-1.0.9-9-9-9.11	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,5,9,2,6,7,3,4,8),\ldots$
8.9-1.0.9-9-9-9.5	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
8.9-1.0.9-9-9-9.9	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,7,5,3,9,4,2,8,6),\ldots$
8.9-1.0.9-9-9-9.4	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
8.9-1.0.9-9-9-9.10	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,5,9,2,6,7,3,4,8),\ldots$
8.9-1.0.9-9-9-9.1	$8$	$0$	$C_9$	$9$	$1$	$[ 0; 9, 9, 9, 9 ]$		$(1,4,7,2,5,8,3,6,9),\ldots$
9.9-1.0.3-3-3-9-9.11	$9$	$0$	$C_9$	$9$	$2$	$[ 0; 3, 3, 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
9.9-1.0.3-3-3-9-9.12	$9$	$0$	$C_9$	$9$	$2$	$[ 0; 3, 3, 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
9.9-1.0.3-3-3-9-9.10	$9$	$0$	$C_9$	$9$	$2$	$[ 0; 3, 3, 3, 9, 9 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$

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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.