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The results below are complete, since the LMFDB contains all groups acting as automorphisms of curves of genus 2, 3 or 4

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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 (8 matches)

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Refined passport label Genus Group Group order Dimension Signature Generating vectors
4.12-5.0.6-6-6.2 $4$ $C_2\times C_6$ $12$ $0$ $[ 0; 6, 6, 6 ]$ $(1,6,2,4,3,5)(7,12,8,10,9,11),\ldots$
4.12-5.0.6-6-6.1 $4$ $C_2\times C_6$ $12$ $0$ $[ 0; 6, 6, 6 ]$ $(1,5,3,4,2,6)(7,11,9,10,8,12),\ldots$
4.12-5.0.2-2-3-6.3 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-5.0.2-2-3-6.4 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-5.0.2-2-3-6.1 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-5.0.2-2-3-6.6 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
4.12-5.0.2-2-3-6.5 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
4.12-5.0.2-2-3-6.2 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
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