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

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Results (1-50 of 248 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
9.16-10.0.4-4-4-4.6	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15),\ldots$
9.16-10.0.4-4-4-4.1	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,9,2,10)(3,11,4,12)(5,13,6,14)(7,15,8,16),\ldots$
9.16-10.0.4-4-4-4.2	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,9,2,10)(3,11,4,12)(5,13,6,14)(7,15,8,16),\ldots$
9.16-10.0.4-4-4-4.8	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15),\ldots$
9.16-10.0.4-4-4-4.3	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,9,2,10)(3,11,4,12)(5,13,6,14)(7,15,8,16),\ldots$
9.16-10.0.4-4-4-4.5	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15),\ldots$
9.16-10.0.4-4-4-4.7	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15),\ldots$
9.16-10.0.4-4-4-4.4	$9$	$0$	$C_2^2\times C_4$	$16$	$1$	$[ 0; 4, 4, 4, 4 ]$	$(1,9,2,10)(3,11,4,12)(5,13,6,14)(7,15,8,16),\ldots$
9.16-10.0.2-2-2-4-4.7	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.12	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.6	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.13	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.14	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.15	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.3	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.11	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.20	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.10	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.5	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.21	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.22	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.23	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.24	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.25	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.26	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.27	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.28	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.29	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.30	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.31	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.19	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.36	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.18	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.9	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.35	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.37	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.38	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.39	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.40	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.41	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.42	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.43	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.44	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.45	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.46	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.47	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.48	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
9.16-10.0.2-2-2-4-4.49	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
9.16-10.0.2-2-2-4-4.50	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
9.16-10.0.2-2-2-4-4.34	$9$	$0$	$C_2^2\times C_4$	$16$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$

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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.