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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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
10.18-5.0.3-3-6-6.132	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,8,6)(2,9,4)(3,7,5)(10,17,15)(11,18,13)(12,16,14),\ldots$
10.18-5.0.3-3-6-6.124	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,6,8)(2,4,9)(3,5,7)(10,15,17)(11,13,18)(12,14,16),\ldots$
10.18-5.0.3-3-6-6.125	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,6,8)(2,4,9)(3,5,7)(10,15,17)(11,13,18)(12,14,16),\ldots$
10.18-5.0.3-3-6-6.126	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,6,8)(2,4,9)(3,5,7)(10,15,17)(11,13,18)(12,14,16),\ldots$
10.18-5.0.3-3-6-6.127	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,6,8)(2,4,9)(3,5,7)(10,15,17)(11,13,18)(12,14,16),\ldots$
10.18-5.0.3-3-6-6.128	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,6,8)(2,4,9)(3,5,7)(10,15,17)(11,13,18)(12,14,16),\ldots$
10.18-5.0.3-3-6-6.129	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,6,8)(2,4,9)(3,5,7)(10,15,17)(11,13,18)(12,14,16),\ldots$
10.18-5.0.3-3-6-6.130	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,8,6)(2,9,4)(3,7,5)(10,17,15)(11,18,13)(12,16,14),\ldots$
10.18-5.0.3-3-6-6.131	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,8,6)(2,9,4)(3,7,5)(10,17,15)(11,18,13)(12,16,14),\ldots$
10.18-5.0.3-3-6-6.7	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.9	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.11	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.13	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.15	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.17	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.19	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.22	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.23	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.26	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.27	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.29	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
10.18-5.0.3-3-6-6.35	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.36	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.39	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.40	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.43	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.45	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.47	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.48	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.51	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.52	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.55	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.57	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
10.18-5.0.3-3-6-6.64	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.65	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.69	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.71	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.72	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.73	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.77	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.79	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18),\ldots$
10.18-5.0.3-3-6-6.85	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.86	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.87	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.88	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.93	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.94	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.95	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.96	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15),\ldots$
10.18-5.0.3-3-6-6.105	$10$	$0$	$C_3\times C_6$	$18$	$1$	$[ 0; 3, 3, 6, 6 ]$	$(1,5,9)(2,6,7)(3,4,8)(10,14,18)(11,15,16)(12,13,17),\ldots$

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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.