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
15.35-1.0.7-35-35.1	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.2	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.4	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.5	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.6	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.7	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.8	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.10	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.11	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.12	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.14	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.15	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.16	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.18	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.19	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.20	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,3,5,7,2,4,6)\cdots(29,31,33,35,30,32,34),\ldots$
15.35-1.0.7-35-35.21	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.23	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.24	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.25	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.27	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.28	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.29	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.30	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,4,7,3,6,2,5)\cdots(29,32,35,31,34,30,33),\ldots$
15.35-1.0.7-35-35.31	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.32	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.33	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.34	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.36	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.37	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.38	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.40	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,5,2,6,3,7,4)\cdots(29,33,30,34,31,35,32),\ldots$
15.35-1.0.7-35-35.42	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.43	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.44	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.46	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.47	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.48	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.49	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.50	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,6,4,2,7,5,3)\cdots(29,34,32,30,35,33,31),\ldots$
15.35-1.0.7-35-35.51	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.52	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.54	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.55	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.56	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.58	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.59	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.60	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,7,6,5,4,3,2)\cdots(29,35,34,33,32,31,30),\ldots$
15.35-1.0.7-35-35.3	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$
15.35-1.0.7-35-35.9	$15$	$0$	$C_{35}$	$35$	$0$	$[ 0; 7, 35, 35 ]$	$(1,2,3,4,5,6,7)\cdots(29,30,31,32,33,34,35),\ldots$

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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.