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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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
11.16-11.0.2-2-4-4-4.1	$11$	$0$	$C_2\times D_4$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-11.0.2-2-4-4-4.2	$11$	$0$	$C_2\times D_4$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
11.16-11.0.2-2-4-4-4.3	$11$	$0$	$C_2\times D_4$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$		$(1,7)(2,8)(3,5)(4,6)(9,15)(10,16)(11,13)(12,14),\ldots$
11.16-11.0.2-2-4-4-4.4	$11$	$0$	$C_2\times D_4$	$16$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$		$(1,7)(2,8)(3,5)(4,6)(9,15)(10,16)(11,13)(12,14),\ldots$
11.16-11.0.2-2-2-2-2-4.1	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.2	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.3	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.4	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.5	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.6	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.7	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.8	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.9	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.10	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.11	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.12	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.13	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.14	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.15	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.16	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.17	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.18	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.19	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.20	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.21	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.22	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.23	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.24	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.25	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.26	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.27	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.28	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
11.16-11.0.2-2-2-2-2-4.29	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.30	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.31	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.32	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.33	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.34	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.35	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.36	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.37	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.38	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.39	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.40	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.41	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.42	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.43	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.44	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.45	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
11.16-11.0.2-2-2-2-2-4.46	$11$	$0$	$C_2\times D_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 2, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$

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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.