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 (40 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
15.20-2.0.4-4-20-20.12	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-4-20-20.8	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-4-20-20.9	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-4-20-20.10	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-4-20-20.11	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.1	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.2	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.3	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.4	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.5	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.6	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.7	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.8	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.9	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.10	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.11	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.12	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-5-10-20.13	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.14	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.15	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.16	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.17	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.18	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.19	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.20	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.21	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.22	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.23	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-5-10-20.24	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 5, 10, 20 ]$		$(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19),\ldots$
15.20-2.0.4-4-20-20.1	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-4-20-20.2	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-4-20-20.3	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-4-20-20.4	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-4-20-20.5	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-4-20-20.6	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.4-4-20-20.7	$15$	$0$	$C_{20}$	$20$	$1$	$[ 0; 4, 4, 20, 20 ]$		$(1,11,2,12)(3,13,4,14)(5,15,6,16)(7,17,8,18)(9,19,10,20),\ldots$
15.20-2.0.2-2-2-20-20.2	$15$	$0$	$C_{20}$	$20$	$2$	$[ 0; 2, 2, 2, 20, 20 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
15.20-2.0.2-2-2-20-20.3	$15$	$0$	$C_{20}$	$20$	$2$	$[ 0; 2, 2, 2, 20, 20 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
15.20-2.0.2-2-2-20-20.4	$15$	$0$	$C_{20}$	$20$	$2$	$[ 0; 2, 2, 2, 20, 20 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$
15.20-2.0.2-2-2-20-20.1	$15$	$0$	$C_{20}$	$20$	$2$	$[ 0; 2, 2, 2, 20, 20 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20),\ldots$

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Overview	Random
Universe	Knowledge

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.