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	Cyclic trigonal	Generating vectors
7.9-2.0.3-3-3-3-3.2	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.4	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.5	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.7	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.8	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.9	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.12	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.14	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.16	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.17	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.21	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.23	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.24	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.25	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.26	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.28	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.29	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.31	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.33	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.34	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
7.9-2.0.3-3-3-3-3.36	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.37	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.39	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.40	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.41	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.44	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.45	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.46	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.48	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.50	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.53	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.54	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.55	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
7.9-2.0.3-3-3-3-3.57	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.58	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.60	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.62	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.64	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.65	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.66	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.68	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.69	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,4,7)(2,5,8)(3,6,9),\ldots$
7.9-2.0.3-3-3-3-3.71	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,7,4)(2,8,5)(3,9,6),\ldots$
7.9-2.0.3-3-3-3-3.73	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,7,4)(2,8,5)(3,9,6),\ldots$
7.9-2.0.3-3-3-3-3.74	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$		$(1,7,4)(2,8,5)(3,9,6),\ldots$
7.9-2.0.3-3-3-3-3.75	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,7,4)(2,8,5)(3,9,6),\ldots$
7.9-2.0.3-3-3-3-3.77	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,5,9)(2,6,7)(3,4,8),\ldots$
7.9-2.0.3-3-3-3-3.78	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,5,9)(2,6,7)(3,4,8),\ldots$
7.9-2.0.3-3-3-3-3.79	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,5,9)(2,6,7)(3,4,8),\ldots$
7.9-2.0.3-3-3-3-3.80	$7$	$0$	$C_3^2$	$9$	$2$	$[ 0; 3, 3, 3, 3, 3 ]$	✓	$(1,9,5)(2,7,6)(3,8,4),\ldots$

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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.