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

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
5.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2.1	$5$	$0$	$C_2$	$2$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2),\ldots$
5.4-1.0.2-2-2-2-2-4-4.1	$5$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
5.4-1.0.2-2-2-2-2-4-4.2	$5$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.12	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.6	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.2	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.1	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.9	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.10	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
5.6-2.0.2-2-2-2-3-3.1	$5$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 2, 2, 3, 3 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
5.8-2.0.2-2-2-4-4.21	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
5.8-2.0.2-2-2-4-4.22	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
5.8-2.0.2-2-2-4-4.4	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.2	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.16	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.15	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-2.0.2-2-2-4-4.3	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-2.0.2-2-2-4-4.1	$5$	$0$	$C_2\times C_4$	$8$	$2$	$[ 0; 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.43	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.39	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.44	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.36	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.45	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.74	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
5.8-5.0.2-2-2-2-2-2.59	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.35	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.30	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.63	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.55	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.41	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.56	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.64	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.2	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.70	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
5.8-5.0.2-2-2-2-2-2.20	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.75	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
5.8-5.0.2-2-2-2-2-2.4	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.76	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
5.8-5.0.2-2-2-2-2-2.21	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.32	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.34	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.31	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.1	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.26	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.8-5.0.2-2-2-2-2-2.57	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
5.8-5.0.2-2-2-2-2-2.3	$5$	$0$	$C_2^3$	$8$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
5.12-1.0.2-3-4-4.2	$5$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 2, 3, 4, 4 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-1.0.2-3-4-4.1	$5$	$0$	$C_3:C_4$	$12$	$1$	$[ 0; 2, 3, 4, 4 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-4.0.2-2-2-2-3.2	$5$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 3 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
5.12-4.0.2-2-2-2-3.1	$5$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 2, 3 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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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.