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 (42 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
14.20-5.0.2-2-2-10-10.1	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.2	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.3	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.4	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.5	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.6	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.7	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.8	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.9	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.10	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.11	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.12	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.13	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.14	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.15	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.16	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.17	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.18	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.19	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.20	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.21	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.22	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.23	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.24	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.25	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.26	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.27	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.28	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.29	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.30	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.31	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.32	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.33	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.34	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.35	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.36	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.37	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.38	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$		$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.39	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$
14.20-5.0.2-2-2-10-10.40	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$
14.20-5.0.2-2-2-10-10.41	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$
14.20-5.0.2-2-2-10-10.42	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$

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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.