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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 (7 matches)

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Refined passport label Genus Group Group order Dimension Signature Generating vectors
4.4-2.0.2-2-2-2-2-2-2.1 $4$ $C_2^2$ $4$ $4$ $[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ $(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.2 $4$ $C_2^2$ $4$ $4$ $[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ $(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.3 $4$ $C_2^2$ $4$ $4$ $[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ $(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.4 $4$ $C_2^2$ $4$ $4$ $[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ $(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.5 $4$ $C_2^2$ $4$ $4$ $[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ $(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.6 $4$ $C_2^2$ $4$ $4$ $[ 0; 2, 2, 2, 2, 2, 2, 2 ]$ $(1,2)(3,4),\ldots$
4.4-2.1.2-2-2.1 $4$ $C_2^2$ $4$ $3$ $[ 1; 2, 2, 2 ]$ $(1,2)(3,4),\ldots$
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