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 (1-50 of 242 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
3.7-1.0.7-7-7.6	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
3.7-1.0.7-7-7.2	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
3.7-1.0.7-7-7.1	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
3.7-1.0.7-7-7.3	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
3.7-1.0.7-7-7.5	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
3.7-1.0.7-7-7.4	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
3.7-1.0.7-7-7.8	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,5,2,6,3,7,4),\ldots$
3.7-1.0.7-7-7.7	$3$	$0$	$C_7$	$7$	$0$	$[ 0; 7, 7, 7 ]$	$(1,5,2,6,3,7,4),\ldots$
6.7-1.0.7-7-7-7.7	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.2	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.8	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.3	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.17	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,5,2,6,3,7,4),\ldots$
6.7-1.0.7-7-7-7.5	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.14	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
6.7-1.0.7-7-7-7.16	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
6.7-1.0.7-7-7-7.9	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
6.7-1.0.7-7-7-7.18	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,6,4,2,7,5,3),\ldots$
6.7-1.0.7-7-7-7.11	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
6.7-1.0.7-7-7-7.1	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.6	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.10	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
6.7-1.0.7-7-7-7.12	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
6.7-1.0.7-7-7-7.4	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
6.7-1.0.7-7-7-7.15	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
6.7-1.0.7-7-7-7.13	$6$	$0$	$C_7$	$7$	$1$	$[ 0; 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.33	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
9.7-1.0.7-7-7-7-7.30	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
9.7-1.0.7-7-7-7-7.31	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
9.7-1.0.7-7-7-7-7.32	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
9.7-1.0.7-7-7-7-7.34	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,5,2,6,3,7,4),\ldots$
9.7-1.0.7-7-7-7-7.27	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.28	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.25	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.24	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.26	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.29	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,4,7,3,6,2,5),\ldots$
9.7-1.0.7-7-7-7-7.35	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,5,2,6,3,7,4),\ldots$
9.7-1.0.7-7-7-7-7.19	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.16	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.20	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.12	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.13	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.15	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.17	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.18	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.10	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.23	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,3,5,7,2,4,6),\ldots$
9.7-1.0.7-7-7-7-7.11	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$
9.7-1.0.7-7-7-7-7.14	$9$	$0$	$C_7$	$7$	$2$	$[ 0; 7, 7, 7, 7, 7 ]$	$(1,2,3,4,5,6,7),\ldots$

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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.