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
12.28-4.0.14-14-14.30	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,14,6,12,4,10,2,8,7,13,5,11,3,9)(15,28,20,26,18,24,16,22,21,27,19,25,17,23),\ldots$
12.28-4.0.14-14-14.12	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,13,4,9,7,12,3,8,6,11,2,14,5,10)(15,27,18,23,21,26,17,22,20,25,16,28,19,24),\ldots$
12.28-4.0.14-14-14.13	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,13,4,9,7,12,3,8,6,11,2,14,5,10)(15,27,18,23,21,26,17,22,20,25,16,28,19,24),\ldots$
12.28-4.0.14-14-14.14	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,13,4,9,7,12,3,8,6,11,2,14,5,10)(15,27,18,23,21,26,17,22,20,25,16,28,19,24),\ldots$
12.28-4.0.14-14-14.15	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,13,4,9,7,12,3,8,6,11,2,14,5,10)(15,27,18,23,21,26,17,22,20,25,16,28,19,24),\ldots$
12.28-4.0.14-14-14.16	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,10,5,14,2,11,6,8,3,12,7,9,4,13)(15,24,19,28,16,25,20,22,17,26,21,23,18,27),\ldots$
12.28-4.0.14-14-14.17	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,10,5,14,2,11,6,8,3,12,7,9,4,13)(15,24,19,28,16,25,20,22,17,26,21,23,18,27),\ldots$
12.28-4.0.14-14-14.18	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,10,5,14,2,11,6,8,3,12,7,9,4,13)(15,24,19,28,16,25,20,22,17,26,21,23,18,27),\ldots$
12.28-4.0.14-14-14.19	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,10,5,14,2,11,6,8,3,12,7,9,4,13)(15,24,19,28,16,25,20,22,17,26,21,23,18,27),\ldots$
12.28-4.0.14-14-14.20	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,10,5,14,2,11,6,8,3,12,7,9,4,13)(15,24,19,28,16,25,20,22,17,26,21,23,18,27),\ldots$
12.28-4.0.14-14-14.21	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,26,16,27,17,28,18,22,19,23,20,24,21,25),\ldots$
12.28-4.0.14-14-14.22	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,26,16,27,17,28,18,22,19,23,20,24,21,25),\ldots$
12.28-4.0.14-14-14.23	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,26,16,27,17,28,18,22,19,23,20,24,21,25),\ldots$
12.28-4.0.14-14-14.24	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,26,16,27,17,28,18,22,19,23,20,24,21,25),\ldots$
12.28-4.0.14-14-14.25	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,26,16,27,17,28,18,22,19,23,20,24,21,25),\ldots$
12.28-4.0.14-14-14.26	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,14,6,12,4,10,2,8,7,13,5,11,3,9)(15,28,20,26,18,24,16,22,21,27,19,25,17,23),\ldots$
12.28-4.0.14-14-14.27	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,14,6,12,4,10,2,8,7,13,5,11,3,9)(15,28,20,26,18,24,16,22,21,27,19,25,17,23),\ldots$
12.28-4.0.14-14-14.28	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,14,6,12,4,10,2,8,7,13,5,11,3,9)(15,28,20,26,18,24,16,22,21,27,19,25,17,23),\ldots$
12.28-4.0.14-14-14.29	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,14,6,12,4,10,2,8,7,13,5,11,3,9)(15,28,20,26,18,24,16,22,21,27,19,25,17,23),\ldots$
12.28-4.0.14-14-14.1	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,9,3,11,5,13,7,8,2,10,4,12,6,14)(15,23,17,25,19,27,21,22,16,24,18,26,20,28),\ldots$
12.28-4.0.14-14-14.2	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,9,3,11,5,13,7,8,2,10,4,12,6,14)(15,23,17,25,19,27,21,22,16,24,18,26,20,28),\ldots$
12.28-4.0.14-14-14.3	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,9,3,11,5,13,7,8,2,10,4,12,6,14)(15,23,17,25,19,27,21,22,16,24,18,26,20,28),\ldots$
12.28-4.0.14-14-14.4	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,9,3,11,5,13,7,8,2,10,4,12,6,14)(15,23,17,25,19,27,21,22,16,24,18,26,20,28),\ldots$
12.28-4.0.14-14-14.5	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,9,3,11,5,13,7,8,2,10,4,12,6,14)(15,23,17,25,19,27,21,22,16,24,18,26,20,28),\ldots$
12.28-4.0.14-14-14.6	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,11,7,10,6,9,5,8,4,14,3,13,2,12)(15,25,21,24,20,23,19,22,18,28,17,27,16,26),\ldots$
12.28-4.0.14-14-14.7	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,11,7,10,6,9,5,8,4,14,3,13,2,12)(15,25,21,24,20,23,19,22,18,28,17,27,16,26),\ldots$
12.28-4.0.14-14-14.8	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,11,7,10,6,9,5,8,4,14,3,13,2,12)(15,25,21,24,20,23,19,22,18,28,17,27,16,26),\ldots$
12.28-4.0.14-14-14.9	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,11,7,10,6,9,5,8,4,14,3,13,2,12)(15,25,21,24,20,23,19,22,18,28,17,27,16,26),\ldots$
12.28-4.0.14-14-14.10	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,11,7,10,6,9,5,8,4,14,3,13,2,12)(15,25,21,24,20,23,19,22,18,28,17,27,16,26),\ldots$
12.28-4.0.14-14-14.11	$12$	$0$	$C_2\times C_{14}$	$28$	$0$	$[ 0; 14, 14, 14 ]$	$(1,13,4,9,7,12,3,8,6,11,2,14,5,10)(15,27,18,23,21,26,17,22,20,25,16,28,19,24),\ldots$
12.28-4.0.2-2-7-14.2	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.3	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.4	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.5	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.6	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.7	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.8	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.9	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.10	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.11	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.12	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$
12.28-4.0.2-2-7-14.13	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,15)\cdots(14,28),\ldots$
12.28-4.0.2-2-7-14.14	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,15)\cdots(14,28),\ldots$
12.28-4.0.2-2-7-14.15	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,15)\cdots(14,28),\ldots$
12.28-4.0.2-2-7-14.16	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,15)\cdots(14,28),\ldots$
12.28-4.0.2-2-7-14.17	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,15)\cdots(14,28),\ldots$
12.28-4.0.2-2-7-14.18	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,15)\cdots(14,28),\ldots$
12.28-4.0.2-2-7-14.1	$12$	$0$	$C_2\times C_{14}$	$28$	$1$	$[ 0; 2, 2, 7, 14 ]$	$(1,8)\cdots(21,28),\ldots$

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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 $\F_{q}$
Belyi maps

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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.