LMFDB - Family of higher genus curves with automorphisms search results

Note: Search results may be incomplete due to uncomputed quantities: hyperelliptic (6913 objects)

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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 155 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
9.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$9$	$0$	$C_2$	$2$	$17$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2),\ldots$
9.4-1.0.2-2-2-2-2-2-2-2-2-4-4.1	$9$	$0$	$C_4$	$4$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
9.4-1.0.2-2-2-2-2-2-2-2-2-4-4.2	$9$	$0$	$C_4$	$4$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.15	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.1	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.20	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.2	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.21	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.25	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
9.6-2.0.2-2-2-2-2-2-6-6.1	$9$	$0$	$C_6$	$6$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
9.8-2.0.2-2-2-2-2-4-4.40	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-2.0.2-2-2-2-2-4-4.3	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-2.0.2-2-2-2-2-4-4.39	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-2.0.2-2-2-2-2-4-4.49	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
9.8-2.0.2-2-2-2-2-4-4.1	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-2.0.2-2-2-2-2-4-4.4	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-2.0.2-2-2-2-2-4-4.2	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-2.0.2-2-2-2-2-4-4.50	$9$	$0$	$C_2\times C_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.2	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.170	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.1	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.161	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.271	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.160	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.293	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.307	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.310	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.312	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.181	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.107	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.269	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.106	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.260	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.157	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.252	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.243	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.154	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.242	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.4	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.191	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.153	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.190	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.3	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.189	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.184	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-5.0.2-2-2-2-2-2-2-2.140	$9$	$0$	$C_2^3$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.10-2.0.2-2-2-2-5-5.2	$9$	$0$	$C_{10}$	$10$	$3$	$[ 0; 2, 2, 2, 2, 5, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
9.10-2.0.2-2-2-2-5-5.1	$9$	$0$	$C_{10}$	$10$	$3$	$[ 0; 2, 2, 2, 2, 5, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
9.12-1.0.2-2-4-4-6.1	$9$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 2, 4, 4, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
9.12-1.0.2-2-4-4-6.2	$9$	$0$	$C_3:C_4$	$12$	$2$	$[ 0; 2, 2, 4, 4, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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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.