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 (1-50 of 140 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
2.5-1.0.5-5-5.3	$2$	$0$	$C_5$	$5$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
2.5-1.0.5-5-5.1	$2$	$0$	$C_5$	$5$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
2.5-1.0.5-5-5.2	$2$	$0$	$C_5$	$5$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
2.5-1.0.5-5-5.4	$2$	$0$	$C_5$	$5$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3),\ldots$
4.5-1.0.5-5-5-5.2	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
4.5-1.0.5-5-5-5.7	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$	$(1,4,2,5,3),\ldots$
4.5-1.0.5-5-5-5.6	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
4.5-1.0.5-5-5-5.1	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
4.5-1.0.5-5-5-5.3	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
4.5-1.0.5-5-5-5.5	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
4.5-1.0.5-5-5-5.4	$4$	$0$	$C_5$	$5$	$1$	$[ 0; 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.11	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,4,2,5,3),\ldots$
6.5-1.0.5-5-5-5-5.10	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
6.5-1.0.5-5-5-5-5.12	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,5,4,3,2),\ldots$
6.5-1.0.5-5-5-5-5.9	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
6.5-1.0.5-5-5-5-5.5	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.8	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
6.5-1.0.5-5-5-5-5.7	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.4	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.3	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.2	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.1	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
6.5-1.0.5-5-5-5-5.6	$6$	$0$	$C_5$	$5$	$2$	$[ 0; 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.14	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
8.5-1.0.5-5-5-5-5-5.13	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
8.5-1.0.5-5-5-5-5-5.12	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
8.5-1.0.5-5-5-5-5-5.11	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.10	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.8	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.15	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
8.5-1.0.5-5-5-5-5-5.9	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.7	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.6	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.5	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.4	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.3	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.2	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
8.5-1.0.5-5-5-5-5-5.16	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,4,2,5,3),\ldots$
8.5-1.0.5-5-5-5-5-5.1	$8$	$0$	$C_5$	$5$	$3$	$[ 0; 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.10	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.9	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.1	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$
10.5-1.0.5-5-5-5-5-5-5.24	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,4,2,5,3),\ldots$
10.5-1.0.5-5-5-5-5-5-5.23	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.22	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.21	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.20	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.19	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.18	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,3,5,2,4),\ldots$
10.5-1.0.5-5-5-5-5-5-5.17	$10$	$0$	$C_5$	$5$	$4$	$[ 0; 5, 5, 5, 5, 5, 5, 5 ]$	$(1,2,3,4,5),\ldots$

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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.