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	Generating vectors
13.8-5.0.2-2-2-2-2-2-2-2-2-2.2	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.3	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.4	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.5	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.6	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.7	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.8	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.9	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.10	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.11	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.12	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.13	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.14	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.15	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.16	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.17	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.18	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.19	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.20	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.21	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.22	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.23	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.24	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.25	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.26	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.27	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.28	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.29	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.30	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.31	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.32	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.33	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.34	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.35	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.36	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.37	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.38	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.39	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.40	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.41	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.42	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.43	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.44	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.45	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.46	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.47	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.48	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.49	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.50	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.1	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$

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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.