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	Generating vectors
6.25-2.0.5-5-5.4	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5)\cdots(21,22,23,24,25),\ldots$
6.25-2.0.5-5-5.5	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5)\cdots(21,22,23,24,25),\ldots$
6.25-2.0.5-5-5.6	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5)\cdots(21,22,23,24,25),\ldots$
6.25-2.0.5-5-5.7	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5)\cdots(21,22,23,24,25),\ldots$
6.25-2.0.5-5-5.8	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5)\cdots(21,22,23,24,25),\ldots$
6.25-2.0.5-5-5.10	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,2,3,4,5)\cdots(21,22,23,24,25),\ldots$
6.25-2.0.5-5-5.11	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.12	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.13	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.14	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.16	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.17	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.18	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.19	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.20	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,3,5,2,4)\cdots(21,23,25,22,24),\ldots$
6.25-2.0.5-5-5.22	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.23	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.24	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.25	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.26	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.28	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.29	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.30	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,4,2,5,3)\cdots(21,24,22,25,23),\ldots$
6.25-2.0.5-5-5.31	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.32	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.34	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.35	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.36	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.37	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.38	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.40	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,5,4,3,2)\cdots(21,25,24,23,22),\ldots$
6.25-2.0.5-5-5.41	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,6,11,16,21)\cdots(5,10,15,20,25),\ldots$
6.25-2.0.5-5-5.42	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,6,11,16,21)\cdots(5,10,15,20,25),\ldots$
6.25-2.0.5-5-5.43	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,6,11,16,21)\cdots(5,10,15,20,25),\ldots$
6.25-2.0.5-5-5.44	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,6,11,16,21)\cdots(5,10,15,20,25),\ldots$
6.25-2.0.5-5-5.46	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,6,11,16,21)\cdots(5,10,15,20,25),\ldots$
6.25-2.0.5-5-5.47	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,11,21,6,16)\cdots(5,15,25,10,20),\ldots$
6.25-2.0.5-5-5.48	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,11,21,6,16)\cdots(5,15,25,10,20),\ldots$
6.25-2.0.5-5-5.49	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,11,21,6,16)\cdots(5,15,25,10,20),\ldots$
6.25-2.0.5-5-5.50	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,11,21,6,16)\cdots(5,15,25,10,20),\ldots$
6.25-2.0.5-5-5.52	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,11,21,6,16)\cdots(5,15,25,10,20),\ldots$
6.25-2.0.5-5-5.53	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,16,6,21,11)\cdots(5,20,10,25,15),\ldots$
6.25-2.0.5-5-5.54	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,16,6,21,11)\cdots(5,20,10,25,15),\ldots$
6.25-2.0.5-5-5.55	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,16,6,21,11)\cdots(5,20,10,25,15),\ldots$
6.25-2.0.5-5-5.56	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,16,6,21,11)\cdots(5,20,10,25,15),\ldots$
6.25-2.0.5-5-5.58	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,16,6,21,11)\cdots(5,20,10,25,15),\ldots$
6.25-2.0.5-5-5.59	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,21,16,11,6)\cdots(5,25,20,15,10),\ldots$
6.25-2.0.5-5-5.60	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,21,16,11,6)\cdots(5,25,20,15,10),\ldots$
6.25-2.0.5-5-5.61	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,21,16,11,6)\cdots(5,25,20,15,10),\ldots$
6.25-2.0.5-5-5.62	$6$	$0$	$C_5^2$	$25$	$0$	$[ 0; 5, 5, 5 ]$	$(1,21,16,11,6)\cdots(5,25,20,15,10),\ldots$

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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.