LMFDB - Family of higher genus curves with automorphisms search results

Note: Search results may be incomplete due to uncomputed quantities: hyperelliptic (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 (1-50 of 116 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
14.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$14$	$0$	$C_2$	$2$	$27$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2),\ldots$
14.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.1	$14$	$0$	$C_4$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.36	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
14.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.29	$14$	$0$	$C_2^2$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
14.6-2.0.2-2-2-2-2-2-2-2-2-2-3-3.1	$14$	$0$	$C_6$	$6$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
14.8-1.0.2-2-2-2-2-2-2-8-8.2	$14$	$0$	$C_8$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 8, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
14.8-4.0.2-2-2-2-2-2-4-4-4.1	$14$	$0$	$Q_8$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
14.8-1.0.2-2-2-2-2-2-2-8-8.1	$14$	$0$	$C_8$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 8, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
14.8-3.0.2-2-2-2-2-2-2-2-2-4.1	$14$	$0$	$D_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
14.10-2.0.2-2-2-2-2-2-5-5.1	$14$	$0$	$C_{10}$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 5, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
14.10-2.0.2-2-2-2-2-2-5-5.2	$14$	$0$	$C_{10}$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 5, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
14.12-5.0.2-2-2-2-2-6-6.2	$14$	$0$	$C_2\times C_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.12-5.0.2-2-2-2-2-6-6.1	$14$	$0$	$C_2\times C_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.12-1.0.2-2-2-2-3-4-4.1	$14$	$0$	$C_3:C_4$	$12$	$4$	$[ 0; 2, 2, 2, 2, 3, 4, 4 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.12-5.0.2-2-2-2-2-6-6.44	$14$	$0$	$C_2\times C_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
14.12-5.0.2-2-2-2-2-6-6.45	$14$	$0$	$C_2\times C_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,10)(2,11)(3,12)(4,7)(5,8)(6,9),\ldots$
14.12-5.0.2-2-2-2-2-6-6.34	$14$	$0$	$C_2\times C_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
14.12-5.0.2-2-2-2-2-6-6.35	$14$	$0$	$C_2\times C_6$	$12$	$4$	$[ 0; 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,7)(2,8)(3,9)(4,10)(5,11)(6,12),\ldots$
14.12-4.0.2-2-2-2-2-2-2-3.1	$14$	$0$	$D_6$	$12$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 3 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
14.14-2.0.2-2-2-2-14-14.3	$14$	$0$	$C_{14}$	$14$	$3$	$[ 0; 2, 2, 2, 2, 14, 14 ]$	✓	$(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14),\ldots$
14.14-2.0.2-2-2-2-14-14.2	$14$	$0$	$C_{14}$	$14$	$3$	$[ 0; 2, 2, 2, 2, 14, 14 ]$	✓	$(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14),\ldots$
14.14-2.0.2-2-2-2-14-14.1	$14$	$0$	$C_{14}$	$14$	$3$	$[ 0; 2, 2, 2, 2, 14, 14 ]$	✓	$(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14),\ldots$
14.16-8.0.2-2-2-2-4-8.2	$14$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.16-8.0.2-2-2-2-4-8.1	$14$	$0$	$\SD_{16}$	$16$	$3$	$[ 0; 2, 2, 2, 2, 4, 8 ]$	✓	$(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16),\ldots$
14.20-5.0.2-2-2-10-10.3	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.2	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.1	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-1.0.2-2-4-4-5.2	$14$	$0$	$C_5:C_4$	$20$	$2$	$[ 0; 2, 2, 4, 4, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.4	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.27	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-1.0.2-2-4-4-5.1	$14$	$0$	$C_5:C_4$	$20$	$2$	$[ 0; 2, 2, 4, 4, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-5.0.2-2-2-10-10.41	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$
14.20-5.0.2-2-2-10-10.40	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$
14.20-5.0.2-2-2-10-10.39	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$
14.20-5.0.2-2-2-10-10.30	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.29	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-5.0.2-2-2-10-10.42	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,16)(2,17)(3,18)(4,19)(5,20)(6,11)(7,12)(8,13)(9,14)(10,15),\ldots$
14.20-5.0.2-2-2-10-10.28	$14$	$0$	$C_2\times C_{10}$	$20$	$2$	$[ 0; 2, 2, 2, 10, 10 ]$	✓	$(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20),\ldots$
14.20-4.0.2-2-2-2-2-5.1	$14$	$0$	$D_{10}$	$20$	$3$	$[ 0; 2, 2, 2, 2, 2, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.20-4.0.2-2-2-2-2-5.2	$14$	$0$	$D_{10}$	$20$	$3$	$[ 0; 2, 2, 2, 2, 2, 5 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20),\ldots$
14.24-8.0.2-2-2-4-6.2	$14$	$0$	$C_3:D_4$	$24$	$2$	$[ 0; 2, 2, 2, 4, 6 ]$	✓	$(1,4)\cdots(21,24),\ldots$
14.24-8.0.2-2-2-4-6.1	$14$	$0$	$C_3:D_4$	$24$	$2$	$[ 0; 2, 2, 2, 4, 6 ]$	✓	$(1,4)\cdots(21,24),\ldots$
14.24-3.0.2-2-3-3-4.1	$14$	$0$	$\SL(2,3)$	$24$	$2$	$[ 0; 2, 2, 3, 3, 4 ]$	✓	$(1,2)\cdots(23,24),\ldots$
14.28-1.0.2-4-4-14.1	$14$	$0$	$C_7:C_4$	$28$	$1$	$[ 0; 2, 4, 4, 14 ]$	✓	$(1,8)\cdots(21,28),\ldots$
14.28-1.0.2-4-4-14.2	$14$	$0$	$C_7:C_4$	$28$	$1$	$[ 0; 2, 4, 4, 14 ]$	✓	$(1,8)\cdots(21,28),\ldots$
14.28-1.0.2-4-4-14.3	$14$	$0$	$C_7:C_4$	$28$	$1$	$[ 0; 2, 4, 4, 14 ]$	✓	$(1,8)\cdots(21,28),\ldots$
14.28-3.0.2-2-2-2-14.1	$14$	$0$	$D_{14}$	$28$	$2$	$[ 0; 2, 2, 2, 2, 14 ]$	✓	$(1,8)\cdots(21,28),\ldots$
14.28-3.0.2-2-2-2-14.3	$14$	$0$	$D_{14}$	$28$	$2$	$[ 0; 2, 2, 2, 2, 14 ]$	✓	$(1,8)\cdots(21,28),\ldots$
14.28-3.0.2-2-2-2-14.2	$14$	$0$	$D_{14}$	$28$	$2$	$[ 0; 2, 2, 2, 2, 14 ]$	✓	$(1,8)\cdots(21,28),\ldots$

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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.