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Note: Search results may be incomplete due to uncomputed quantities: cyclic_trigonal (6913 objects)

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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 (32 matches)

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Refined passport label Genus Group Group order Dimension Signature Generating vectors
4.3-1.0.3-3-3-3-3-3.2 $4$ $C_3$ $3$ $3$ $[ 0; 3, 3, 3, 3, 3, 3 ]$ $(1,2,3),\ldots$
4.3-1.0.3-3-3-3-3-3.3 $4$ $C_3$ $3$ $3$ $[ 0; 3, 3, 3, 3, 3, 3 ]$ $(1,3,2),\ldots$
4.3-1.0.3-3-3-3-3-3.1 $4$ $C_3$ $3$ $3$ $[ 0; 3, 3, 3, 3, 3, 3 ]$ $(1,2,3),\ldots$
4.6-2.0.2-2-3-3-3.2 $4$ $C_6$ $6$ $2$ $[ 0; 2, 2, 3, 3, 3 ]$ $(1,4)(2,5)(3,6),\ldots$
4.6-1.0.2-2-3-3-3.1 $4$ $S_3$ $6$ $2$ $[ 0; 2, 2, 3, 3, 3 ]$ $(1,4)(2,6)(3,5),\ldots$
4.6-2.0.2-2-3-3-3.1 $4$ $C_6$ $6$ $2$ $[ 0; 2, 2, 3, 3, 3 ]$ $(1,4)(2,5)(3,6),\ldots$
4.12-5.0.2-2-3-6.2 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
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 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.12-5.0.2-2-3-6.5 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
4.12-5.0.2-2-3-6.6 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
4.12-4.0.2-2-3-6.1 $4$ $D_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,7)(2,9)(3,8)(4,10)(5,12)(6,11),\ldots$
4.12-5.0.2-2-3-6.1 $4$ $C_2\times C_6$ $12$ $1$ $[ 0; 2, 2, 3, 6 ]$ $(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
4.15-1.0.3-5-15.5 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
4.15-1.0.3-5-15.7 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
4.15-1.0.3-5-15.4 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
4.15-1.0.3-5-15.6 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
4.15-1.0.3-5-15.8 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10),\ldots$
4.15-1.0.3-5-15.2 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
4.15-1.0.3-5-15.3 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
4.15-1.0.3-5-15.1 $4$ $C_{15}$ $15$ $0$ $[ 0; 3, 5, 15 ]$ $(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15),\ldots$
4.18-3.0.2-2-3-3.1 $4$ $C_3\times S_3$ $18$ $1$ $[ 0; 2, 2, 3, 3 ]$ $(1,10)(2,12)(3,11)(4,13)(5,15)(6,14)(7,16)(8,18)(9,17),\ldots$
4.18-3.0.2-2-3-3.2 $4$ $C_3\times S_3$ $18$ $1$ $[ 0; 2, 2, 3, 3 ]$ $(1,10)(2,12)(3,11)(4,13)(5,15)(6,14)(7,16)(8,18)(9,17),\ldots$
4.36-12.0.2-6-6.2 $4$ $C_6\times S_3$ $36$ $0$ $[ 0; 2, 6, 6 ]$ $(1,19)\cdots(18,35),\ldots$
4.36-12.0.2-6-6.4 $4$ $C_6\times S_3$ $36$ $0$ $[ 0; 2, 6, 6 ]$ $(1,28)\cdots(18,26),\ldots$
4.36-12.0.2-6-6.3 $4$ $C_6\times S_3$ $36$ $0$ $[ 0; 2, 6, 6 ]$ $(1,28)\cdots(18,26),\ldots$
4.36-12.0.2-6-6.1 $4$ $C_6\times S_3$ $36$ $0$ $[ 0; 2, 6, 6 ]$ $(1,19)\cdots(18,35),\ldots$
4.36-10.0.2-2-2-3.1 $4$ $S_3^2$ $36$ $1$ $[ 0; 2, 2, 2, 3 ]$ $(1,10)\cdots(27,33),\ldots$
4.72-40.0.2-4-6.2 $4$ $\SOPlus(4,2)$ $72$ $0$ $[ 0; 2, 4, 6 ]$ $(1,37)\cdots(36,60),\ldots$
4.72-42.0.2-3-12.1 $4$ $C_3\times S_4$ $72$ $0$ $[ 0; 2, 3, 12 ]$ $(1,37)\cdots(36,68),\ldots$
4.72-40.0.2-4-6.1 $4$ $\SOPlus(4,2)$ $72$ $0$ $[ 0; 2, 4, 6 ]$ $(1,19)\cdots(54,72),\ldots$
4.72-42.0.2-3-12.2 $4$ $C_3\times S_4$ $72$ $0$ $[ 0; 2, 3, 12 ]$ $(1,37)\cdots(36,68),\ldots$
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