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 (30 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
4.10-1.0.2-2-5-5.2	$4$	$0$	$D_5$	$10$	$1$	$[ 0; 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
4.10-1.0.2-2-5-5.1	$4$	$0$	$D_5$	$10$	$1$	$[ 0; 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
4.10-1.0.2-2-5-5.3	$4$	$0$	$D_5$	$10$	$1$	$[ 0; 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
5.10-1.0.2-2-2-2-5.1	$5$	$0$	$D_5$	$10$	$2$	$[ 0; 2, 2, 2, 2, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
5.10-1.0.2-2-2-2-5.2	$5$	$0$	$D_5$	$10$	$2$	$[ 0; 2, 2, 2, 2, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
6.10-1.0.2-2-2-2-2-2.1	$6$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
8.10-1.0.2-2-5-5-5.1	$8$	$0$	$D_5$	$10$	$2$	$[ 0; 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
8.10-1.0.2-2-5-5-5.2	$8$	$0$	$D_5$	$10$	$2$	$[ 0; 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
8.10-1.0.2-2-5-5-5.3	$8$	$0$	$D_5$	$10$	$2$	$[ 0; 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
8.10-1.0.2-2-5-5-5.4	$8$	$0$	$D_5$	$10$	$2$	$[ 0; 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
9.10-1.0.2-2-2-2-5-5.1	$9$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
9.10-1.0.2-2-2-2-5-5.2	$9$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
9.10-1.0.2-2-2-2-5-5.3	$9$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
10.10-1.0.2-2-2-2-2-2-5.1	$10$	$0$	$D_5$	$10$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
10.10-1.0.2-2-2-2-2-2-5.2	$10$	$0$	$D_5$	$10$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
11.10-1.0.2-2-2-2-2-2-2-2.1	$11$	$0$	$D_5$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
12.10-1.0.2-2-5-5-5-5.1	$12$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 5, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
12.10-1.0.2-2-5-5-5-5.2	$12$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 5, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
12.10-1.0.2-2-5-5-5-5.3	$12$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 5, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
12.10-1.0.2-2-5-5-5-5.4	$12$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 5, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
12.10-1.0.2-2-5-5-5-5.5	$12$	$0$	$D_5$	$10$	$3$	$[ 0; 2, 2, 5, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
13.10-1.0.2-2-2-2-5-5-5.1	$13$	$0$	$D_5$	$10$	$4$	$[ 0; 2, 2, 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
13.10-1.0.2-2-2-2-5-5-5.2	$13$	$0$	$D_5$	$10$	$4$	$[ 0; 2, 2, 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
13.10-1.0.2-2-2-2-5-5-5.3	$13$	$0$	$D_5$	$10$	$4$	$[ 0; 2, 2, 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
13.10-1.0.2-2-2-2-5-5-5.4	$13$	$0$	$D_5$	$10$	$4$	$[ 0; 2, 2, 2, 2, 5, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
14.10-1.0.2-2-2-2-2-2-5-5.1	$14$	$0$	$D_5$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
14.10-1.0.2-2-2-2-2-2-5-5.2	$14$	$0$	$D_5$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
14.10-1.0.2-2-2-2-2-2-5-5.3	$14$	$0$	$D_5$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 5, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
15.10-1.0.2-2-2-2-2-2-2-2-5.1	$15$	$0$	$D_5$	$10$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$
15.10-1.0.2-2-2-2-2-2-2-2-5.2	$15$	$0$	$D_5$	$10$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 5 ]$	$(1,6)(2,10)(3,9)(4,8)(5,7),\ldots$

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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.