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 159 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
13.16-3.0.2-4-4-4-4.1	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-4-4-4-4.2	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-4-4-4-4.3	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-4-4-4-4.4	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-4-4-4-4.5	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
13.16-3.0.2-4-4-4-4.6	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
13.16-3.0.2-4-4-4-4.7	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
13.16-3.0.2-4-4-4-4.8	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
13.16-3.0.2-4-4-4-4.9	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
13.16-3.0.2-4-4-4-4.10	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
13.16-3.0.2-4-4-4-4.11	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
13.16-3.0.2-4-4-4-4.12	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
13.16-3.0.2-4-4-4-4.13	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
13.16-3.0.2-4-4-4-4.14	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.15	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.16	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.17	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.18	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.19	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.20	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.21	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16),\ldots$
13.16-3.0.2-4-4-4-4.22	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-4-4-4-4.23	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-4-4-4-4.24	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-4-4-4-4.25	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-4-4-4-4.26	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-4-4-4-4.27	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-4-4-4-4.28	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-4-4-4-4.29	$13$	$0$	$C_2^2:C_4$	$16$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15),\ldots$
13.16-3.0.2-2-2-2-4-4.1	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.2	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.3	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.4	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.5	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.6	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.7	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.8	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.9	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.10	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.11	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.12	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.13	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.14	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.15	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.16	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.17	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.18	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.21	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.19	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
13.16-3.0.2-2-2-2-4-4.20	$13$	$0$	$C_2^2:C_4$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$

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Overview	Random
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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.