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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Results (48 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
13.32-25.0.2-4-4-4.2	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.25	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.26	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.27	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.28	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.1	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.3	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.4	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.5	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.6	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.7	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.8	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.9	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.10	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.11	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.12	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,9)\cdots(24,32),\ldots$
13.32-25.0.2-4-4-4.13	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.14	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.15	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.16	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.17	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.18	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.19	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.20	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.21	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.22	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.23	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.24	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,10)\cdots(24,31),\ldots$
13.32-25.0.2-4-4-4.29	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.30	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.31	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.32	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.33	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.34	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.35	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.36	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,21)\cdots(16,25),\ldots$
13.32-25.0.2-4-4-4.37	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.38	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.39	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.40	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.41	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.42	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.43	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.44	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.45	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.46	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.47	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$
13.32-25.0.2-4-4-4.48	$13$	$0$	$C_4\times D_4$	$32$	$1$	$[ 0; 2, 4, 4, 4 ]$	$(1,22)\cdots(16,26),\ldots$

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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.