LMFDB - Family of higher genus curves with automorphisms search results

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Genus	Dimension of the family	Group order	Hyperelliptic curves	Full automorphism group

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Results (1-50 of 312 matches)

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Refined passport label	Genus	Quotient genus	Group	Group order	Dimension	Signature	Hyperelliptic	Generating vectors
2.4-2.0.2-2-2-2-2.1	$2$	$0$	$C_2^2$	$4$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
2.4-2.0.2-2-2-2-2.3	$2$	$0$	$C_2^2$	$4$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
2.4-2.0.2-2-2-2-2.2	$2$	$0$	$C_2^2$	$4$	$2$	$[ 0; 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.6	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
3.4-2.0.2-2-2-2-2-2.7	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
3.4-2.0.2-2-2-2-2-2.4	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.2	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.5	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.3	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
3.4-2.0.2-2-2-2-2-2.1	$3$	$0$	$C_2^2$	$4$	$3$	$[ 0; 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
3.4-2.1.2-2.3	$3$	$1$	$C_2^2$	$4$	$2$	$[ 1; 2, 2 ]$		$(1,2)(3,4),\ldots$
3.4-2.1.2-2.1	$3$	$1$	$C_2^2$	$4$	$2$	$[ 1; 2, 2 ]$		$(1,2)(3,4),\ldots$
3.4-2.1.2-2.2	$3$	$1$	$C_2^2$	$4$	$2$	$[ 1; 2, 2 ]$		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.1	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.5	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.4	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.3	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.2	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
4.4-2.0.2-2-2-2-2-2-2.6	$4$	$0$	$C_2^2$	$4$	$4$	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
4.4-2.1.2-2-2.1	$4$	$1$	$C_2^2$	$4$	$3$	$[ 1; 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.4	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.2	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.3	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.12	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.11	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.10	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.9	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.8	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.7	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.1	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.5	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
5.4-2.0.2-2-2-2-2-2-2-2.6	$5$	$0$	$C_2^2$	$4$	$5$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.10	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.8	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.9	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.3	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.6	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.1	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.4	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.5	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.7	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
6.4-2.0.2-2-2-2-2-2-2-2-2.2	$6$	$0$	$C_2^2$	$4$	$6$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.18	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.16	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.17	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,3)(2,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.12	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.15	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,3)(2,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.14	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.13	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$		$(1,2)(3,4),\ldots$
7.4-2.0.2-2-2-2-2-2-2-2-2-2.2	$7$	$0$	$C_2^2$	$4$	$7$	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$	✓	$(1,2)(3,4),\ldots$

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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.