LMFDB - Family of higher genus curves with automorphisms search results

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
5.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2.1	$5$	$0$	$C_2$	$2$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.1	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.2	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.3	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.4	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.5	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.6	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.7	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.8	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.9	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.10	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.11	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.12	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.13	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.14	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.15	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.17	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.18	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.19	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.20	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.21	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,3)(2,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.22	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,3)(2,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.23	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,3)(2,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.24	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,3)(2,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.25	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,3)(2,4),\ldots$
9.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2.16	$9$	$0$	$C_2^2$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.1	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.2	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.3	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.4	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
10.3-1.0.3-3-3-3-3-3-3-3-3-3-3-3.5	$10$	$0$	$C_3$	$3$	$9$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,3,2),\ldots$
10.4-1.0.2-2-2-2-2-2-2-2-2-2-4-4.1	$10$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
11.4-1.0.2-2-2-2-2-2-2-2-4-4-4-4.2	$11$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
11.4-1.0.2-2-2-2-2-2-2-2-4-4-4-4.1	$11$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
11.4-1.0.2-2-2-2-2-2-2-2-4-4-4-4.3	$11$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
12.4-1.0.2-2-2-2-2-2-4-4-4-4-4-4.1	$12$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
12.4-1.0.2-2-2-2-2-2-4-4-4-4-4-4.2	$12$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
12.4-1.0.2-2-2-2-2-2-4-4-4-4-4-4.3	$12$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
13.4-1.0.2-2-2-2-4-4-4-4-4-4-4-4.3	$13$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
13.4-1.0.2-2-2-2-4-4-4-4-4-4-4-4.1	$13$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
13.4-1.0.2-2-2-2-4-4-4-4-4-4-4-4.2	$13$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
13.4-1.0.2-2-2-2-4-4-4-4-4-4-4-4.4	$13$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
13.4-1.0.2-2-2-2-4-4-4-4-4-4-4-4.5	$13$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
13.6-1.0.2-2-2-2-2-2-2-2-2-2-2-2.1	$13$	$0$	$S_3$	$6$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$			$(1,4)(2,6)(3,5),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.1	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.4	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.3	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.5	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
14.4-1.0.2-2-4-4-4-4-4-4-4-4-4-4.2	$14$	$0$	$C_4$	$4$	$9$	$[ 0; 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
14.6-2.0.2-2-2-2-2-2-2-2-2-2-3-3.1	$14$	$0$	$C_6$	$6$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]$	✓		$(1,4)(2,5)(3,6),\ldots$

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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.