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 (36 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
15.24-5.0.4-4-4-12.1	$15$	$0$	$C_4\times S_3$	$24$	$1$	$[ 0; 4, 4, 4, 12 ]$		$(1,7,4,10)\cdots(15,21,18,24),\ldots$
15.24-5.0.4-4-4-12.2	$15$	$0$	$C_4\times S_3$	$24$	$1$	$[ 0; 4, 4, 4, 12 ]$		$(1,7,4,10)\cdots(15,21,18,24),\ldots$
15.24-5.0.4-4-4-12.3	$15$	$0$	$C_4\times S_3$	$24$	$1$	$[ 0; 4, 4, 4, 12 ]$		$(1,7,4,10)\cdots(15,21,18,24),\ldots$
15.24-5.0.4-4-4-12.4	$15$	$0$	$C_4\times S_3$	$24$	$1$	$[ 0; 4, 4, 4, 12 ]$		$(1,10,4,7)\cdots(15,24,18,21),\ldots$
15.24-5.0.4-4-4-12.5	$15$	$0$	$C_4\times S_3$	$24$	$1$	$[ 0; 4, 4, 4, 12 ]$		$(1,10,4,7)\cdots(15,24,18,21),\ldots$
15.24-5.0.4-4-4-12.6	$15$	$0$	$C_4\times S_3$	$24$	$1$	$[ 0; 4, 4, 4, 12 ]$		$(1,10,4,7)\cdots(15,24,18,21),\ldots$
15.24-5.0.2-2-3-4-4.7	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-3-4-4.8	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-3-4-4.9	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-3-4-4.10	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-3-4-4.11	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,16)\cdots(12,20),\ldots$
15.24-5.0.2-2-3-4-4.12	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,16)\cdots(12,20),\ldots$
15.24-5.0.2-2-2-4-12.1	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$	✓	$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.2	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$	✓	$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.3	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$	✓	$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.4	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$	✓	$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.5	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.6	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-3-4-4.1	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.8	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.9	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.10	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-2-4-12.11	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-2-4-12.12	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-2-4-12.13	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-2-4-12.14	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-2-4-12.15	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-2-4-12.16	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-2-4-12.17	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,16)\cdots(12,20),\ldots$
15.24-5.0.2-2-2-4-12.18	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,16)\cdots(12,20),\ldots$
15.24-5.0.2-2-2-4-12.7	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 2, 4, 12 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-3-4-4.2	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-3-4-4.3	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-3-4-4.4	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,4)\cdots(21,24),\ldots$
15.24-5.0.2-2-3-4-4.5	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,13)\cdots(12,23),\ldots$
15.24-5.0.2-2-3-4-4.6	$15$	$0$	$C_4\times S_3$	$24$	$2$	$[ 0; 2, 2, 3, 4, 4 ]$		$(1,13)\cdots(12,23),\ldots$

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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.