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 325 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
2.10-2.0.2-5-10.2	$2$	$0$	$C_{10}$	$10$	$0$	$[ 0; 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
2.10-2.0.2-5-10.4	$2$	$0$	$C_{10}$	$10$	$0$	$[ 0; 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
2.10-2.0.2-5-10.3	$2$	$0$	$C_{10}$	$10$	$0$	$[ 0; 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
2.10-2.0.2-5-10.1	$2$	$0$	$C_{10}$	$10$	$0$	$[ 0; 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
4.10-2.0.5-10-10.2	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
4.10-2.0.5-10-10.1	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
4.10-2.0.5-10-10.5	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,4,2,5,3)(6,9,7,10,8),\ldots$
4.10-2.0.5-10-10.3	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,3,5,2,4)(6,8,10,7,9),\ldots$
4.10-2.0.5-10-10.7	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,5,4,3,2)(6,10,9,8,7),\ldots$
4.10-2.0.5-10-10.6	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,4,2,5,3)(6,9,7,10,8),\ldots$
4.10-2.0.5-10-10.8	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,5,4,3,2)(6,10,9,8,7),\ldots$
4.10-2.0.5-10-10.4	$4$	$0$	$C_{10}$	$10$	$0$	$[ 0; 5, 10, 10 ]$		$(1,3,5,2,4)(6,8,10,7,9),\ldots$
4.10-2.0.2-2-5-5.1	$4$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 2, 5, 5 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
4.10-2.0.2-2-5-5.2	$4$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 2, 5, 5 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
5.10-2.0.2-2-10-10.2	$5$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
5.10-2.0.2-2-10-10.1	$5$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.6	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.5	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.3	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.2	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.8	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.7	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.1	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
6.10-2.0.2-5-5-10.4	$6$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 5, 5, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-10-10-10.1	$7$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 10, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-10-10-10.2	$7$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 10, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-10-10-10.3	$7$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 10, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-10-10-10.4	$7$	$0$	$C_{10}$	$10$	$1$	$[ 0; 2, 10, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-2-2-5-10.1	$7$	$0$	$C_{10}$	$10$	$2$	$[ 0; 2, 2, 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-2-2-5-10.2	$7$	$0$	$C_{10}$	$10$	$2$	$[ 0; 2, 2, 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-2-2-5-10.3	$7$	$0$	$C_{10}$	$10$	$2$	$[ 0; 2, 2, 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
7.10-2.0.2-2-2-5-10.4	$7$	$0$	$C_{10}$	$10$	$2$	$[ 0; 2, 2, 2, 5, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
8.10-2.0.5-5-10-10.16	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,4,2,5,3)(6,9,7,10,8),\ldots$
8.10-2.0.5-5-10-10.11	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,3,5,2,4)(6,8,10,7,9),\ldots$
8.10-2.0.5-5-10-10.19	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,5,4,3,2)(6,10,9,8,7),\ldots$
8.10-2.0.5-5-10-10.2	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
8.10-2.0.5-5-10-10.18	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,4,2,5,3)(6,9,7,10,8),\ldots$
8.10-2.0.5-5-10-10.7	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
8.10-2.0.5-5-10-10.13	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,3,5,2,4)(6,8,10,7,9),\ldots$
8.10-2.0.5-5-10-10.14	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,3,5,2,4)(6,8,10,7,9),\ldots$
8.10-2.0.5-5-10-10.6	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
8.10-2.0.5-5-10-10.10	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,3,5,2,4)(6,8,10,7,9),\ldots$
8.10-2.0.5-5-10-10.15	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,4,2,5,3)(6,9,7,10,8),\ldots$
8.10-2.0.5-5-10-10.17	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,4,2,5,3)(6,9,7,10,8),\ldots$
8.10-2.0.5-5-10-10.20	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,5,4,3,2)(6,10,9,8,7),\ldots$
8.10-2.0.5-5-10-10.12	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,3,5,2,4)(6,8,10,7,9),\ldots$
8.10-2.0.5-5-10-10.8	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
8.10-2.0.5-5-10-10.1	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
8.10-2.0.5-5-10-10.3	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$
8.10-2.0.5-5-10-10.4	$8$	$0$	$C_{10}$	$10$	$1$	$[ 0; 5, 5, 10, 10 ]$		$(1,2,3,4,5)(6,7,8,9,10),\ldots$

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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.