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 160 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Generating vectors
15.31-1.0.31-31-31.6	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.7	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.8	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.2	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.3	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.4	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.9	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.10	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.11	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.12	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.13	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.14	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,2,3,4,5,6,7,8,9,10,\ldots),\ldots$
15.31-1.0.31-31-31.17	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.18	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.19	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.20	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.21	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.22	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.23	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.25	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.26	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.27	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.28	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,3,5,7,9,11,13,15,17,19,\ldots),\ldots$
15.31-1.0.31-31-31.31	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.32	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.33	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.34	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.35	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.36	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.37	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.38	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.39	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.42	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,4,7,10,13,16,19,22,25,28,\ldots),\ldots$
15.31-1.0.31-31-31.44	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.45	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.47	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.48	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.49	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.50	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.51	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.52	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.53	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,5,9,13,17,21,25,29,2,6,\ldots),\ldots$
15.31-1.0.31-31-31.56	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$
15.31-1.0.31-31-31.57	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$
15.31-1.0.31-31-31.58	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$
15.31-1.0.31-31-31.59	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$
15.31-1.0.31-31-31.60	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$
15.31-1.0.31-31-31.61	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$
15.31-1.0.31-31-31.62	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$
15.31-1.0.31-31-31.64	$15$	$0$	$C_{31}$	$31$	$0$	$[ 0; 31, 31, 31 ]$	$(1,6,11,16,21,26,31,5,10,15,\ldots),\ldots$

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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.