Family of higher genus curves with automorphisms search results

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

Results (1-50 of 53 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Cyclic trigonal	Generating vectors
6.3-1.0.3-3-3-3-3-3-3-3.3	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.1	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
6.3-1.0.3-3-3-3-3-3-3-3.2	$6$	$0$	$C_3$	$3$	$5$	$[ 0; 3, 3, 3, 3, 3, 3, 3, 3 ]$		✓	$(1,2,3),\ldots$
6.6-2.0.3-3-3-6-6.4	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,3,2)(4,6,5),\ldots$
6.6-2.0.3-3-3-6-6.1	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-2.0.3-3-3-6-6.2	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-2.0.3-3-3-6-6.3	$6$	$0$	$C_6$	$6$	$2$	$[ 0; 3, 3, 3, 6, 6 ]$		✓	$(1,2,3)(4,5,6),\ldots$
6.6-1.0.2-2-3-3-3-3.1	$6$	$0$	$S_3$	$6$	$3$	$[ 0; 2, 2, 3, 3, 3, 3 ]$		✓	$(1,4)(2,6)(3,5),\ldots$
6.6-2.0.2-2-3-3-3-3.1	$6$	$0$	$C_6$	$6$	$3$	$[ 0; 2, 2, 3, 3, 3, 3 ]$		✓	$(1,4)(2,5)(3,6),\ldots$
6.9-1.0.3-3-9-9.9	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
6.9-1.0.3-3-9-9.8	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
6.9-1.0.3-3-9-9.2	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.1	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.9-1.0.3-3-9-9.7	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		✓	$(1,3,2)(4,6,5)(7,9,8),\ldots$
6.9-1.0.3-3-9-9.3	$6$	$0$	$C_9$	$9$	$1$	$[ 0; 3, 3, 9, 9 ]$		✓	$(1,2,3)(4,5,6)(7,8,9),\ldots$
6.12-5.0.2-3-6-6.4	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$		✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
6.12-5.0.2-3-6-6.6	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$		✓	$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
6.12-5.0.2-3-6-6.3	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$		✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
6.12-5.0.2-3-6-6.5	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$		✓	$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
6.12-5.0.2-3-6-6.2	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-5.0.2-3-6-6.1	$6$	$0$	$C_2\times C_6$	$12$	$1$	$[ 0; 2, 3, 6, 6 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-4.0.2-2-2-3-3.1	$6$	$0$	$D_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 3 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.12-5.0.2-2-2-3-3.1	$6$	$0$	$C_2\times C_6$	$12$	$2$	$[ 0; 2, 2, 2, 3, 3 ]$		✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
6.18-2.0.3-18-18.5	$6$	$0$	$C_{18}$	$18$	$0$	$[ 0; 3, 18, 18 ]$		✓	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
6.18-2.0.3-18-18.2	$6$	$0$	$C_{18}$	$18$	$0$	$[ 0; 3, 18, 18 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
6.18-2.0.3-18-18.1	$6$	$0$	$C_{18}$	$18$	$0$	$[ 0; 3, 18, 18 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
6.18-2.0.3-18-18.6	$6$	$0$	$C_{18}$	$18$	$0$	$[ 0; 3, 18, 18 ]$		✓	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
6.18-2.0.3-18-18.4	$6$	$0$	$C_{18}$	$18$	$0$	$[ 0; 3, 18, 18 ]$		✓	$(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17),\ldots$
6.18-2.0.3-18-18.3	$6$	$0$	$C_{18}$	$18$	$0$	$[ 0; 3, 18, 18 ]$		✓	$(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18),\ldots$
6.18-1.0.2-2-3-9.3	$6$	$0$	$D_9$	$18$	$1$	$[ 0; 2, 2, 3, 9 ]$		✓	$(1,10)(2,12)(3,11)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13),\ldots$
6.18-1.0.2-2-3-9.2	$6$	$0$	$D_9$	$18$	$1$	$[ 0; 2, 2, 3, 9 ]$		✓	$(1,10)(2,12)(3,11)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13),\ldots$
6.18-1.0.2-2-3-9.1	$6$	$0$	$D_9$	$18$	$1$	$[ 0; 2, 2, 3, 9 ]$		✓	$(1,10)(2,12)(3,11)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13),\ldots$
6.21-2.0.3-7-21.1	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,8,15)\cdots(7,14,21),\ldots$
6.21-2.0.3-7-21.2	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,8,15)\cdots(7,14,21),\ldots$
6.21-2.0.3-7-21.3	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,8,15)\cdots(7,14,21),\ldots$
6.21-2.0.3-7-21.4	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,8,15)\cdots(7,14,21),\ldots$
6.21-2.0.3-7-21.5	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,8,15)\cdots(7,14,21),\ldots$
6.21-2.0.3-7-21.7	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,15,8)\cdots(7,21,14),\ldots$
6.21-2.0.3-7-21.8	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,15,8)\cdots(7,21,14),\ldots$
6.21-2.0.3-7-21.9	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,15,8)\cdots(7,21,14),\ldots$
6.21-2.0.3-7-21.10	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,15,8)\cdots(7,21,14),\ldots$
6.21-2.0.3-7-21.11	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,15,8)\cdots(7,21,14),\ldots$
6.21-2.0.3-7-21.12	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,15,8)\cdots(7,21,14),\ldots$
6.21-2.0.3-7-21.6	$6$	$0$	$C_{21}$	$21$	$0$	$[ 0; 3, 7, 21 ]$		✓	$(1,8,15)\cdots(7,14,21),\ldots$
6.24-8.0.2-2-3-4.1	$6$	$0$	$C_3:D_4$	$24$	$1$	$[ 0; 2, 2, 3, 4 ]$		✓	$(1,7)\cdots(18,24),\ldots$
6.24-6.0.2-2-3-4.1	$6$	$0$	$D_{12}$	$24$	$1$	$[ 0; 2, 2, 3, 4 ]$		✓	$(1,13)\cdots(12,20),\ldots$
6.48-15.0.2-6-8.1	$6$	$0$	$C_3:D_8$	$48$	$0$	$[ 0; 2, 6, 8 ]$		✓	$(1,25)\cdots(24,41),\ldots$
6.48-15.0.2-6-8.4	$6$	$0$	$C_3:D_8$	$48$	$0$	$[ 0; 2, 6, 8 ]$		✓	$(1,25)\cdots(24,41),\ldots$
6.48-15.0.2-6-8.3	$6$	$0$	$C_3:D_8$	$48$	$0$	$[ 0; 2, 6, 8 ]$		✓	$(1,25)\cdots(24,41),\ldots$
6.48-15.0.2-6-8.2	$6$	$0$	$C_3:D_8$	$48$	$0$	$[ 0; 2, 6, 8 ]$		✓	$(1,25)\cdots(24,41),\ldots$

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