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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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
2.8-4.0.4-4-4.1	$2$	$0$	$Q_8$	$8$	$0$	$[ 0; 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
3.8-4.1.2.1	$3$	$1$	$Q_8$	$8$	$1$	$[ 1; 2 ]$		$(1,5,2,6)(3,8,4,7),\ldots$
4.8-4.0.2-4-4-4.1	$4$	$0$	$Q_8$	$8$	$1$	$[ 0; 2, 4, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-4.0.4-4-4-4.2	$5$	$0$	$Q_8$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
5.8-4.0.4-4-4-4.3	$5$	$0$	$Q_8$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,5,2,6)(3,8,4,7),\ldots$
5.8-4.0.4-4-4-4.1	$5$	$0$	$Q_8$	$8$	$1$	$[ 0; 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
6.8-4.0.2-2-4-4-4.1	$6$	$0$	$Q_8$	$8$	$2$	$[ 0; 2, 2, 4, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-4.0.2-4-4-4-4.3	$7$	$0$	$Q_8$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-4.0.2-4-4-4-4.1	$7$	$0$	$Q_8$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-4.0.2-4-4-4-4.2	$7$	$0$	$Q_8$	$8$	$2$	$[ 0; 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
8.8-4.0.4-4-4-4-4.2	$8$	$0$	$Q_8$	$8$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
8.8-4.0.4-4-4-4-4.3	$8$	$0$	$Q_8$	$8$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
8.8-4.0.4-4-4-4-4.1	$8$	$0$	$Q_8$	$8$	$2$	$[ 0; 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
8.8-4.0.2-2-2-4-4-4.1	$8$	$0$	$Q_8$	$8$	$3$	$[ 0; 2, 2, 2, 4, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-4.0.2-2-4-4-4-4.3	$9$	$0$	$Q_8$	$8$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-4.0.2-2-4-4-4-4.2	$9$	$0$	$Q_8$	$8$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
9.8-4.0.2-2-4-4-4-4.1	$9$	$0$	$Q_8$	$8$	$3$	$[ 0; 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
10.8-4.0.2-4-4-4-4-4.3	$10$	$0$	$Q_8$	$8$	$3$	$[ 0; 2, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
10.8-4.0.2-4-4-4-4-4.2	$10$	$0$	$Q_8$	$8$	$3$	$[ 0; 2, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
10.8-4.0.2-4-4-4-4-4.1	$10$	$0$	$Q_8$	$8$	$3$	$[ 0; 2, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
10.8-4.0.2-2-2-2-4-4-4.1	$10$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 2, 2, 2, 4, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-4.0.4-4-4-4-4-4.7	$11$	$0$	$Q_8$	$8$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$		$(1,5,2,6)(3,8,4,7),\ldots$
11.8-4.0.4-4-4-4-4-4.3	$11$	$0$	$Q_8$	$8$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
11.8-4.0.4-4-4-4-4-4.4	$11$	$0$	$Q_8$	$8$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
11.8-4.0.4-4-4-4-4-4.5	$11$	$0$	$Q_8$	$8$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
11.8-4.0.4-4-4-4-4-4.6	$11$	$0$	$Q_8$	$8$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$		$(1,5,2,6)(3,8,4,7),\ldots$
11.8-4.0.4-4-4-4-4-4.1	$11$	$0$	$Q_8$	$8$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
11.8-4.0.4-4-4-4-4-4.2	$11$	$0$	$Q_8$	$8$	$3$	$[ 0; 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
11.8-4.0.2-2-2-4-4-4-4.1	$11$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-4.0.2-2-2-4-4-4-4.3	$11$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-4.0.2-2-2-4-4-4-4.2	$11$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
12.8-4.0.2-2-4-4-4-4-4.1	$12$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 2, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
12.8-4.0.2-2-4-4-4-4-4.3	$12$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 2, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
12.8-4.0.2-2-4-4-4-4-4.2	$12$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 2, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
12.8-4.0.2-2-2-2-2-4-4-4.1	$12$	$0$	$Q_8$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 4, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-4-4-4-4-4-4.2	$13$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-4-4-4-4-4-4.1	$13$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-4-4-4-4-4-4.3	$13$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-4-4-4-4-4-4.4	$13$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-4-4-4-4-4-4.5	$13$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-4-4-4-4-4-4.6	$13$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-4-4-4-4-4-4.7	$13$	$0$	$Q_8$	$8$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-2-2-2-4-4-4-4.1	$13$	$0$	$Q_8$	$8$	$5$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-2-2-2-4-4-4-4.2	$13$	$0$	$Q_8$	$8$	$5$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-4.0.2-2-2-2-4-4-4-4.3	$13$	$0$	$Q_8$	$8$	$5$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
14.8-4.0.4-4-4-4-4-4-4.4	$14$	$0$	$Q_8$	$8$	$4$	$[ 0; 4, 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
14.8-4.0.4-4-4-4-4-4-4.5	$14$	$0$	$Q_8$	$8$	$4$	$[ 0; 4, 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
14.8-4.0.4-4-4-4-4-4-4.6	$14$	$0$	$Q_8$	$8$	$4$	$[ 0; 4, 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
14.8-4.0.4-4-4-4-4-4-4.1	$14$	$0$	$Q_8$	$8$	$4$	$[ 0; 4, 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$
14.8-4.0.4-4-4-4-4-4-4.2	$14$	$0$	$Q_8$	$8$	$4$	$[ 0; 4, 4, 4, 4, 4, 4, 4 ]$		$(1,3,2,4)(5,7,6,8),\ldots$

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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.