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 192 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
13.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$13$	$0$	$C_2$	$2$	$25$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2),\ldots$
13.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.1	$13$	$0$	$C_4$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
13.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.2	$13$	$0$	$C_4$	$4$	$12$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
13.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.2	$13$	$0$	$C_2^2$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
13.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.28	$13$	$0$	$C_2^2$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
13.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.35	$13$	$0$	$C_2^2$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
13.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$13$	$0$	$C_2^2$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
13.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.36	$13$	$0$	$C_2^2$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
13.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.42	$13$	$0$	$C_2^2$	$4$	$13$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
13.6-2.0.2-2-2-2-2-2-2-2-2-3-6.1	$13$	$0$	$C_6$	$6$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
13.6-2.0.2-2-2-2-2-2-2-2-2-3-6.2	$13$	$0$	$C_6$	$6$	$8$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.2	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.4	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.73	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.1	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.74	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.87	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.88	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
13.8-2.0.2-2-2-2-2-2-2-4-4.3	$13$	$0$	$C_2\times C_4$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.518	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.514	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.508	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.478	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.364	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.365	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.507	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.1	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.908	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.870	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.519	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.4	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.810	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.794	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.774	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.3	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.745	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.744	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.589	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.588	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.587	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.578	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.813	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.574	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.902	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.548	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.911	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,5)(2,6)(3,7)(4,8),\ldots$
13.8-5.0.2-2-2-2-2-2-2-2-2-2.2	$13$	$0$	$C_2^3$	$8$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
13.14-2.0.2-2-2-2-7-7.3	$13$	$0$	$C_{14}$	$14$	$3$	$[ 0; 2, 2, 2, 2, 7, 7 ]$	✓	$(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14),\ldots$
13.14-2.0.2-2-2-2-7-7.2	$13$	$0$	$C_{14}$	$14$	$3$	$[ 0; 2, 2, 2, 2, 7, 7 ]$	✓	$(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14),\ldots$
13.14-2.0.2-2-2-2-7-7.1	$13$	$0$	$C_{14}$	$14$	$3$	$[ 0; 2, 2, 2, 2, 7, 7 ]$	✓	$(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14),\ldots$

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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.