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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Results (48 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
15.16-12.0.4-4-4-4-4.1	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.2	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.3	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.4	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.5	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.6	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.7	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.8	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16),\ldots$
15.16-12.0.4-4-4-4-4.9	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,7,2,8)(3,5,4,6)(9,15,10,16)(11,13,12,14),\ldots$
15.16-12.0.4-4-4-4-4.10	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,7,2,8)(3,5,4,6)(9,15,10,16)(11,13,12,14),\ldots$
15.16-12.0.4-4-4-4-4.11	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,7,2,8)(3,5,4,6)(9,15,10,16)(11,13,12,14),\ldots$
15.16-12.0.4-4-4-4-4.12	$15$	$0$	$C_2\times Q_8$	$16$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$	$(1,7,2,8)(3,5,4,6)(9,15,10,16)(11,13,12,14),\ldots$
15.16-12.0.2-2-2-4-4-4.1	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.2	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.3	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.4	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.5	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.6	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.7	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.8	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.9	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.10	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.11	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.12	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.13	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.14	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.15	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.16	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.17	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.18	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.19	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.20	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
15.16-12.0.2-2-2-4-4-4.21	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.22	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.23	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.24	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.25	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.26	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.27	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.28	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.29	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.30	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.31	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.32	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
15.16-12.0.2-2-2-4-4-4.33	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
15.16-12.0.2-2-2-4-4-4.34	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
15.16-12.0.2-2-2-4-4-4.35	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
15.16-12.0.2-2-2-4-4-4.36	$15$	$0$	$C_2\times Q_8$	$16$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	$(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$

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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.