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 187 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
11.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$11$	$0$	$C_2$	$2$	$21$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2),\ldots$
11.4-1.0.2-2-2-2-2-2-2-2-2-2-2-4-4.1	$11$	$0$	$C_4$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
11.4-1.0.2-2-2-2-2-2-2-2-2-2-2-4-4.2	$11$	$0$	$C_4$	$4$	$10$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4),\ldots$
11.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2.28	$11$	$0$	$C_2^2$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
11.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2.2	$11$	$0$	$C_2^2$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
11.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2.1	$11$	$0$	$C_2^2$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
11.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2.27	$11$	$0$	$C_2^2$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
11.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2.33	$11$	$0$	$C_2^2$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
11.4-2.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2.21	$11$	$0$	$C_2^2$	$4$	$11$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
11.6-2.0.2-2-2-2-2-2-2-2-3-3.1	$11$	$0$	$C_6$	$6$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]$	✓	$(1,4)(2,5)(3,6),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.2	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.3	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.47	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.4	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.65	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.48	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.1	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-2.0.2-2-2-2-2-2-4-4.66	$11$	$0$	$C_2\times C_4$	$8$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 4, 4 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.281	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.280	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.279	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.270	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.181	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.256	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.4	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.276	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.511	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.3	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.473	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.310	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.469	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.461	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.2	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.415	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.414	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.343	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.342	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.444	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4)(5,7)(6,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.336	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.335	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.332	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.494	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.1	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.517	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.525	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,4)(2,3)(5,8)(6,7),\ldots$
11.8-5.0.2-2-2-2-2-2-2-2-2.180	$11$	$0$	$C_2^3$	$8$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4)(5,6)(7,8),\ldots$
11.12-5.0.2-2-2-2-6-6.2	$11$	$0$	$C_2\times C_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 6, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-5.0.2-2-2-2-6-6.1	$11$	$0$	$C_2\times C_6$	$12$	$3$	$[ 0; 2, 2, 2, 2, 6, 6 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-1.0.2-2-2-3-4-4.2	$11$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 4 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$
11.12-1.0.2-2-2-3-4-4.1	$11$	$0$	$C_3:C_4$	$12$	$3$	$[ 0; 2, 2, 2, 3, 4, 4 ]$	✓	$(1,4)(2,5)(3,6)(7,10)(8,11)(9,12),\ldots$

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Classical	Maass
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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.