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	Cyclic trigonal	Generating vectors
3.2-1.1.2-2-2-2.1	$3$	$1$	$C_2$	$2$	$4$	$[ 1; 2, 2, 2, 2 ]$			$(1,2),\ldots$
4.4-2.0.2-2-2-2-2-2-2.3	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.1	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.2	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.5	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.6	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.4	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4),\ldots$
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	$5$	$0$	$C_3$	$3$	$4$	$[ 0; 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
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	$5$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 4, 4 ]$	✓		$(1,2)(3,4),\ldots$
6.4-1.0.2-2-2-4-4-4-4.2	$6$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
6.4-1.0.2-2-2-4-4-4-4.1	$6$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 2, 2, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
6.6-1.0.2-2-2-2-2-2-3.1	$6$	$0$	$S_3$	$6$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 3 ]$			$(1,4)(2,6)(3,5),\ldots$
7.4-1.0.2-4-4-4-4-4-4.3	$7$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
7.4-1.0.2-4-4-4-4-4-4.2	$7$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
7.4-1.0.2-4-4-4-4-4-4.1	$7$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
7.4-1.0.2-4-4-4-4-4-4.4	$7$	$0$	$C_4$	$4$	$4$	$[ 0; 2, 4, 4, 4, 4, 4, 4 ]$			$(1,2)(3,4),\ldots$
7.6-2.0.2-2-2-2-3-3-3.1	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-1.0.2-2-2-2-3-3-3.1	$7$	$0$	$S_3$	$6$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$			$(1,4)(2,6)(3,5),\ldots$
7.6-2.0.2-2-2-2-3-3-3.2	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 3, 3, 3 ]$			$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-2-2-3-6.1	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
7.6-2.0.2-2-2-2-2-3-6.2	$7$	$0$	$C_6$	$6$	$4$	$[ 0; 2, 2, 2, 2, 2, 3, 6 ]$	✓		$(1,4)(2,5)(3,6),\ldots$
7.8-5.0.2-2-2-2-2-2-2.24	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.36	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.34	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.38	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.25	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.23	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.22	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.32	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.31	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.30	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.29	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.4	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.33	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.28	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.35	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-3.0.2-2-2-2-2-2-2.3	$7$	$0$	$D_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.37	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.2	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.39	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-3.0.2-2-2-2-2-2-2.1	$7$	$0$	$D_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.1	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-3.0.2-2-2-2-2-2-2.2	$7$	$0$	$D_4$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.27	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.26	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.3	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓		$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.21	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$
7.8-5.0.2-2-2-2-2-2-2.20	$7$	$0$	$C_2^3$	$8$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$			$(1,2)(3,4)(5,6)(7,8),\ldots$

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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.