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 57 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Cyclic trigonal	Generating vectors
2.3-1.0.3-3-3-3.1	$2$	$0$	$C_3$	$3$	$1$	$[ 0; 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
3.3-1.0.3-3-3-3-3.2	$3$	$0$	$C_3$	$3$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
3.3-1.0.3-3-3-3-3.1	$3$	$0$	$C_3$	$3$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
3.3-1.1.3-3.1	$3$	$1$	$C_3$	$3$	$2$	$[ 1; 3, 3 ]$		$(1,2,3),\ldots$
4.3-1.0.3-3-3-3-3-3.2	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
4.3-1.0.3-3-3-3-3-3.3	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2),\ldots$
4.3-1.0.3-3-3-3-3-3.1	$4$	$0$	$C_3$	$3$	$3$	$[ 0; 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
4.3-1.1.3-3-3.2	$4$	$1$	$C_3$	$3$	$3$	$[ 1; 3, 3, 3 ]$		$(1,2,3),\ldots$
4.3-1.1.3-3-3.1	$4$	$1$	$C_3$	$3$	$3$	$[ 1; 3, 3, 3 ]$		$(1,2,3),\ldots$
4.3-1.2.0.1	$4$	$2$	$C_3$	$3$	$3$	$[ 2; -]$		$(1,2,3),\ldots$
5.3-1.0.3-3-3-3-3-3-3.2	$5$	$0$	$C_3$	$3$	$4$	$[ 0; 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
5.3-1.0.3-3-3-3-3-3-3.1	$5$	$0$	$C_3$	$3$	$4$	$[ 0; 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.3	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.2	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.1	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
7.3-1.0.3-3-3-3-3-3-3-3-3.2	$7$	$0$	$C_3$	$3$	$6$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
7.3-1.0.3-3-3-3-3-3-3-3-3.4	$7$	$0$	$C_3$	$3$	$6$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2),\ldots$
7.3-1.0.3-3-3-3-3-3-3-3-3.3	$7$	$0$	$C_3$	$3$	$6$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
7.3-1.0.3-3-3-3-3-3-3-3-3.1	$7$	$0$	$C_3$	$3$	$6$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
8.3-1.0.3-3-3-3-3-3-3-3-3-3.2	$8$	$0$	$C_3$	$3$	$7$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
8.3-1.0.3-3-3-3-3-3-3-3-3-3.1	$8$	$0$	$C_3$	$3$	$7$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
8.3-1.0.3-3-3-3-3-3-3-3-3-3.3	$8$	$0$	$C_3$	$3$	$7$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
9.3-1.0.3-3-3-3-3-3-3-3-3-3-3.2	$9$	$0$	$C_3$	$3$	$8$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
9.3-1.0.3-3-3-3-3-3-3-3-3-3-3.1	$9$	$0$	$C_3$	$3$	$8$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
9.3-1.0.3-3-3-3-3-3-3-3-3-3-3.4	$9$	$0$	$C_3$	$3$	$8$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
9.3-1.0.3-3-3-3-3-3-3-3-3-3-3.3	$9$	$0$	$C_3$	$3$	$8$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.4	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.1	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.3	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.5	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.2	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
11.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3.2	$11$	$0$	$C_3$	$3$	$10$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
11.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3.1	$11$	$0$	$C_3$	$3$	$10$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
11.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3.3	$11$	$0$	$C_3$	$3$	$10$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
11.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3.4	$11$	$0$	$C_3$	$3$	$10$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
12.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3.3	$12$	$0$	$C_3$	$3$	$11$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
12.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3.4	$12$	$0$	$C_3$	$3$	$11$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
12.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3.5	$12$	$0$	$C_3$	$3$	$11$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
12.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3.2	$12$	$0$	$C_3$	$3$	$11$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
12.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3.1	$12$	$0$	$C_3$	$3$	$11$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
13.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.3	$13$	$0$	$C_3$	$3$	$12$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
13.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.4	$13$	$0$	$C_3$	$3$	$12$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
13.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.1	$13$	$0$	$C_3$	$3$	$12$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,2,3),\ldots$
13.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.2	$13$	$0$	$C_3$	$3$	$12$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
13.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.5	$13$	$0$	$C_3$	$3$	$12$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
13.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.6	$13$	$0$	$C_3$	$3$	$12$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$	✓	$(1,3,2),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.3	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.1	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.2	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$
14.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3.4	$14$	$0$	$C_3$	$3$	$13$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		$(1,2,3),\ldots$

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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.