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
12.15-1.0.5-5-15-15.1	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.3	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.4	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.5	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.6	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.7	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.8	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.9	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.14	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.15	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.21	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.22	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.23	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.24	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,4,2,5,3)(6,9,7,10,8)(11,14,12,15,13),\ldots$
12.15-1.0.5-5-15-15.26	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,4,2,5,3)(6,9,7,10,8)(11,14,12,15,13),\ldots$
12.15-1.0.5-5-15-15.27	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,4,2,5,3)(6,9,7,10,8)(11,14,12,15,13),\ldots$
12.15-1.0.5-5-15-15.28	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,4,2,5,3)(6,9,7,10,8)(11,14,12,15,13),\ldots$
12.15-1.0.5-5-15-15.29	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,4,2,5,3)(6,9,7,10,8)(11,14,12,15,13),\ldots$
12.15-1.0.5-5-15-15.31	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12),\ldots$
12.15-1.0.5-5-15-15.32	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12),\ldots$
12.15-1.0.3-15-15-15.1	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.2	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.3	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.4	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.5	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.6	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.7	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.8	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
12.15-1.0.3-15-15-15.9	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.3-15-15-15.10	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.3-15-15-15.11	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.3-15-15-15.12	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.3-15-15-15.13	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.3-15-15-15.14	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.3-15-15-15.15	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.3-15-15-15.16	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 3, 15, 15, 15 ]$	$(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
12.15-1.0.5-5-15-15.2	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.11	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.12	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.20	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.25	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,4,2,5,3)(6,9,7,10,8)(11,14,12,15,13),\ldots$
12.15-1.0.5-5-15-15.10	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.13	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15),\ldots$
12.15-1.0.5-5-15-15.30	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12),\ldots$
12.15-1.0.5-5-15-15.18	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.16	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.17	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$
12.15-1.0.5-5-15-15.19	$12$	$0$	$C_{15}$	$15$	$1$	$[ 0; 5, 5, 15, 15 ]$	$(1,3,5,2,4)(6,8,10,7,9)(11,13,15,12,14),\ldots$

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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.