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 375 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
2.6-2.0.3-6-6.1	$2$	$0$	$C_6$	$6$	$0$	$[ 0; 3, 6, 6 ]$			$(1,2,3)(4,5,6),\ldots$
2.6-2.0.3-6-6.2	$2$	$0$	$C_6$	$6$	$0$	$[ 0; 3, 6, 6 ]$			$(1,3,2)(4,6,5),\ldots$
2.6-2.0.2-2-3-3.1	$2$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 2, 3, 3 ]$			$(1,4)(2,5)(3,6),\ldots$
3.6-2.0.2-3-3-6.2	$3$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
3.6-2.0.2-2-6-6.1	$3$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 2, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
3.6-2.0.2-3-3-6.1	$3$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.3-3-6-6.2	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 3, 3, 6, 6 ]$			$(1,2,3)(4,5,6),\ldots$
4.6-2.0.3-3-6-6.1	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 3, 3, 6, 6 ]$			$(1,2,3)(4,5,6),\ldots$
4.6-2.0.3-3-6-6.3	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 3, 3, 6, 6 ]$			$(1,3,2)(4,6,5),\ldots$
4.6-2.0.2-6-6-6.2	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.2-6-6-6.1	$4$	$0$	$C_6$	$6$	$1$	$[ 0; 2, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.2-2-2-3-6.2	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.2-2-3-3-3.2	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.2-2-2-3-6.1	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
4.6-2.0.2-2-3-3-3.1	$4$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
4.6-2.1.2-2.1	$4$	$1$	$C_6$	$6$	$2$	$[ 1; 2, 2 ]$			$(1,4)(2,5)(3,6),\ldots$
5.6-2.0.6-6-6-6.1	$5$	$0$	$C_6$	$6$	$1$	$[ 0; 6, 6, 6, 6 ]$			$(1,5,3,4,2,6),\ldots$
5.6-2.0.2-3-3-3-6.2	$5$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 3, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
5.6-2.0.2-3-3-3-6.1	$5$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 3, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
5.6-2.0.2-2-3-6-6.2	$5$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 3, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
5.6-2.0.2-2-3-6-6.1	$5$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 2, 3, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
5.6-2.0.2-2-2-2-3-3.1	$5$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.3-3-3-6-6.3	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-2.0.3-3-3-6-6.2	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-2.0.3-3-3-6-6.1	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-2.0.3-3-3-6-6.4	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,3,2)(4,6,5),\ldots$
6.6-2.0.2-3-6-6-6.1	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 3, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-3-6-6-6.2	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 2, 3, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-2-2-2-6-6.1	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 2, 6, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-2-2-3-3-6.1	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 3, 3, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-2-2-3-3-6.2	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 3, 3, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
6.6-2.0.2-2-3-3-3-3.1	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 3, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.3-6-6-6-6.4	$7$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 6, 6, 6, 6 ]$			$(1,3,2)(4,6,5),\ldots$
7.6-2.0.3-6-6-6-6.2	$7$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 6, 6, 6, 6 ]$			$(1,2,3)(4,5,6),\ldots$
7.6-2.0.3-6-6-6-6.3	$7$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 6, 6, 6, 6 ]$			$(1,3,2)(4,6,5),\ldots$
7.6-2.0.3-6-6-6-6.1	$7$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 6, 6, 6, 6 ]$			$(1,2,3)(4,5,6),\ldots$
7.6-2.0.2-3-3-3-3-6.1	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 3, 3, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-6-6-6.1	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-3-3-6-6.3	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 3, 3, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-3-3-3-3-6.4	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 3, 3, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-6-6-6.2	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-3-3-3-3-6.2	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 3, 3, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-3-3-3-3-6.3	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 3, 3, 3, 3, 6 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-3-3-6-6.2	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 3, 3, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-3-3-6-6.1	$7$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 3, 3, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-2-3-3-3.2	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-2-2-3-6.1	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-2-2-3-6.2	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-2-3-3-3.1	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$			$(1,4)(2,5)(3,6),\ldots$
8.6-2.0.2-2-6-6-6-6.1	$8$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 6, 6, 6, 6 ]$			$(1,4)(2,5)(3,6),\ldots$

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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.