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 245 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
15.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$15$	$0$	$C_2$	$2$	$29$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2),\ldots$
15.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.2	$15$	$0$	$C_4$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
15.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.1	$15$	$0$	$C_4$	$4$	$14$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
15.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.45	$15$	$0$	$C_2^2$	$4$	$15$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
15.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.2	$15$	$0$	$C_2^2$	$4$	$15$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
15.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$15$	$0$	$C_2^2$	$4$	$15$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
15.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.44	$15$	$0$	$C_2^2$	$4$	$15$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
15.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.52	$15$	$0$	$C_2^2$	$4$	$15$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
15.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.36	$15$	$0$	$C_2^2$	$4$	$15$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
15.6-2.0.2-2-2-2-2-2-2-2-2-2-6-6.1	$15$	$0$	$C_6$	$6$	$9$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.2	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.3	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.83	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.4	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.107	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.84	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.1	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-2.0.2-2-2-2-2-2-2-2-4-4.108	$15$	$0$	$C_2\times C_4$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.821	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.820	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.819	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.805	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.567	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.775	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.566	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.815	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1334	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.4	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1273	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.890	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1260	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1224	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.3	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1154	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.951	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.935	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.950	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1155	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.940	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.939	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.2	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1280	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1370	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1380	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.1393	$15$	$0$	$C_2^3$	$8$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
15.10-2.0.2-2-2-2-2-2-10-10.2	$15$	$0$	$C_{10}$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
15.10-2.0.2-2-2-2-2-2-10-10.1	$15$	$0$	$C_{10}$	$10$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 10, 10 ]$	✓	$(1,6)(2,7)(3,8)(4,9)(5,10),\ldots$
15.12-1.0.2-2-2-2-4-4-6.2	$15$	$0$	$C_3:C_4$	$12$	$4$	$[ 0; 2, 2, 2, 2, 4, 4, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
15.12-1.0.2-2-2-2-4-4-6.1	$15$	$0$	$C_3:C_4$	$12$	$4$	$[ 0; 2, 2, 2, 2, 4, 4, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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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.