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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Results (28 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.2	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.3	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.4	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.5	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.6	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.7	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.8	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.9	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.10	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.11	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.12	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.13	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.14	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.15	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.16	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.17	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.18	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.19	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.20	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.21	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.22	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.23	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.24	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.25	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.26	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.27	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
12.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.28	$12$	$0$	$C_2^2$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$

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Overview	Random
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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.