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Degree	Group	Orders	$[a,b,c]$ triple

Genus	Orbit size	Passport size	Base field

Geometry type	Primitive	Primitivization

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Results (27 matches)

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Label	Degree	Group	abc	Ramification type	Genus	Orbit Size	Base field	Triples	Primitivization
5T1-5_5_5-a	$5$	5T1	$[5, 5, 5]$	$[[5], [5], [5]]$	$2$	$1$	$\Q$	$[[[2, 3, 4, 5, 1], [4, 5, 1, 2, 3], [2, 3, 4, 5, 1]]]$	5T1-5_5_5-a
5T1-5_5_5-b	$5$	5T1	$[5, 5, 5]$	$[[5], [5], [5]]$	$2$	$1$	$\Q$	$[[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [4, 5, 1, 2, 3]]]$	5T1-5_5_5-b
5T1-5_5_5-c	$5$	5T1	$[5, 5, 5]$	$[[5], [5], [5]]$	$2$	$1$	$\Q$	$[[[2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2]]]$	5T1-5_5_5-c
5T4-5_5_5-a	$5$	5T4	$[5, 5, 5]$	$[[5], [5], [5]]$	$2$	$1$	$\Q$	$[[[2, 3, 4, 5, 1], [3, 5, 4, 2, 1], [2, 5, 4, 1, 3]]]$	5T4-5_5_5-a
6T1-6_6_3.3-a	$6$	6T1	$[6, 6, 3]$	$[[6], [6], [3, 3]]$	$2$	$1$	$\Q$	$[[[2, 3, 4, 5, 6, 1], [2, 3, 4, 5, 6, 1], [5, 6, 1, 2, 3, 4]]]$	2T1-2_2_1.1-a
6T5-6_6_3.3-a	$6$	6T5	$[6, 6, 3]$	$[[6], [6], [3, 3]]$	$2$	$1$	$\Q$	$[[[6, 5, 2, 1, 4, 3], [6, 1, 2, 3, 4, 5], [5, 4, 1, 6, 3, 2]]]$	2T1-2_2_1.1-a
6T6-6_6_3.3-a	$6$	6T6	$[6, 6, 3]$	$[[6], [6], [3, 3]]$	$2$	$1$	$\Q$	$[[[6, 4, 5, 3, 1, 2], [3, 1, 5, 6, 4, 2], [3, 4, 5, 6, 1, 2]]]$	3T1-3_3_3-a
6T14-6_6_3.3-a	$6$	6T14	$[6, 6, 3]$	$[[6], [6], [3, 3]]$	$2$	$1$	$\Q$	$[[[6, 4, 2, 1, 3, 5], [3, 5, 4, 6, 1, 2], [3, 1, 2, 6, 4, 5]]]$	6T14-6_6_3.3-a
6T14-6_6_5.1-a	$6$	6T14	$[6, 6, 5]$	$[[6], [6], [5, 1]]$	$2$	$1$	$\Q$	$[[[6, 4, 2, 1, 3, 5], [2, 3, 6, 1, 4, 5], [5, 2, 6, 1, 3, 4]]]$	6T14-6_6_5.1-a
6T16-6_6_4.2-a	$6$	6T16	$[6, 6, 4]$	$[[6], [6], [4, 2]]$	$2$	$4$	4.2.8640.2	$[[[6, 3, 4, 5, 1, 2], [3, 5, 6, 2, 1, 4], [2, 3, 4, 1, 6, 5]], [[3, 6, 4, 5, 2, 1], [3, 6, 5, 1, 2, 4], [2, 3, 4, 1, 6, 5]], [[3, 6, 5, 2, 4, 1], [5, 6, 4, 1, 2, 3], [2, 3, 4, 1, 6, 5]], [[2, 4, 6, 5, 3, 1], [2, 6, 1, 5, 3, 4], [2, 3, 4, 1, 6, 5]]]$	6T16-6_6_4.2-a
6T16-6_6_5.1-a	$6$	6T16	$[6, 6, 5]$	$[[6], [6], [5, 1]]$	$2$	$1$	$\Q$	$[[[3, 4, 5, 1, 6, 2], [3, 4, 6, 1, 2, 5], [2, 3, 4, 5, 1, 6]]]$	6T16-6_6_5.1-a
6T16-6_6_5.1-b	$6$	6T16	$[6, 6, 5]$	$[[6], [6], [5, 1]]$	$2$	$6$	6.2.3240000.1	$[[[2, 3, 4, 5, 6, 1], [4, 6, 1, 2, 3, 5], [2, 3, 4, 5, 1, 6]], [[3, 5, 4, 2, 6, 1], [2, 6, 4, 1, 3, 5], [2, 3, 4, 5, 1, 6]], [[4, 3, 5, 2, 6, 1], [3, 6, 4, 2, 1, 5], [2, 3, 4, 5, 1, 6]], [[2, 4, 1, 5, 6, 3], [4, 3, 1, 6, 2, 5], [2, 3, 4, 5, 1, 6]], [[2, 4, 6, 5, 3, 1], [4, 6, 1, 5, 2, 3], [2, 3, 4, 5, 1, 6]], [[4, 5, 1, 2, 6, 3], [2, 3, 4, 6, 1, 5], [2, 3, 4, 5, 1, 6]]]$	6T16-6_6_5.1-b
7T4-7_6.1_6.1-a	$7$	7T4	$[7, 6, 6]$	$[[7], [6, 1], [6, 1]]$	$2$	$2$	$\Q(\sqrt{-3}) $	$[[[2, 3, 4, 5, 6, 7, 1], [2, 5, 1, 4, 7, 3, 6], [5, 3, 1, 6, 4, 2, 7]], [[2, 3, 4, 5, 6, 7, 1], [4, 2, 7, 5, 3, 1, 6], [3, 6, 2, 5, 1, 4, 7]]]$	7T4-7_6.1_6.1-a
7T5-7_7_3.3.1-a	$7$	7T5	$[7, 7, 3]$	$[[7], [7], [3, 3, 1]]$	$2$	$2$	$\Q(\sqrt{-7}) $	$[[[4, 5, 6, 7, 1, 2, 3], [4, 7, 2, 5, 6, 3, 1], [4, 5, 2, 7, 3, 6, 1]], [[2, 3, 4, 5, 6, 7, 1], [2, 7, 1, 6, 3, 5, 4], [2, 3, 1, 5, 7, 6, 4]]]$	7T5-7_7_3.3.1-a
7T5-7_7_3.3.1-b	$7$	7T5	$[7, 7, 3]$	$[[7], [7], [3, 3, 1]]$	$2$	$2$	$\Q(\sqrt{-7}) $	$[[[4, 5, 6, 7, 1, 2, 3], [5, 3, 1, 2, 7, 4, 6], [1, 7, 5, 3, 4, 2, 6]], [[3, 7, 2, 1, 6, 4, 5], [4, 5, 6, 7, 1, 2, 3], [1, 7, 5, 3, 4, 2, 6]]]$	7T5-7_7_3.3.1-b
7T5-7_7_4.2.1-a	$7$	7T5	$[7, 7, 4]$	$[[7], [7], [4, 2, 1]]$	$2$	$4$	$\Q(\sqrt{2}, \sqrt{-7})$	$[[[2, 3, 4, 5, 6, 7, 1], [3, 4, 2, 6, 1, 7, 5], [6, 5, 3, 1, 2, 7, 4]], [[3, 7, 2, 1, 6, 4, 5], [6, 7, 1, 2, 3, 4, 5], [6, 5, 3, 1, 2, 7, 4]], [[7, 6, 5, 2, 1, 3, 4], [7, 3, 6, 1, 4, 5, 2], [6, 5, 3, 1, 2, 7, 4]], [[7, 3, 4, 1, 6, 2, 5], [3, 7, 2, 1, 6, 4, 5], [6, 5, 3, 1, 2, 7, 4]]]$	7T5-7_7_4.2.1-a
7T6-7_7_3.2.2-a	$7$	7T6	$[7, 7, 6]$	$[[7], [7], [3, 2, 2]]$	$2$	$1$	$\Q$	$[[[2, 3, 4, 6, 7, 5, 1], [2, 7, 1, 6, 3, 5, 4], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_7_3.2.2-a
7T6-7_7_3.2.2-b	$7$	7T6	$[7, 7, 6]$	$[[7], [7], [3, 2, 2]]$	$2$	$2$	$\Q(\sqrt{21}) $	$[[[7, 4, 5, 3, 6, 1, 2], [4, 6, 7, 3, 2, 1, 5], [2, 3, 1, 5, 4, 7, 6]], [[4, 5, 7, 3, 6, 1, 2], [4, 6, 7, 2, 1, 3, 5], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_7_3.2.2-b
7T6-7_7_3.2.2-c	$7$	7T6	$[7, 7, 6]$	$[[7], [7], [3, 2, 2]]$	$2$	$2$	$\Q(\sqrt{7}) $	$[[[7, 5, 4, 2, 6, 1, 3], [7, 6, 4, 2, 3, 1, 5], [2, 3, 1, 5, 4, 7, 6]], [[7, 3, 6, 2, 1, 5, 4], [2, 5, 4, 6, 7, 1, 3], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_7_3.2.2-c
7T6-7_7_3.2.2-d	$7$	7T6	$[7, 7, 6]$	$[[7], [7], [3, 2, 2]]$	$2$	$2$	$\Q(\sqrt{-1}) $	$[[[7, 3, 4, 6, 1, 5, 2], [2, 5, 7, 6, 3, 1, 4], [2, 3, 1, 5, 4, 7, 6]], [[2, 4, 6, 3, 7, 5, 1], [4, 7, 1, 6, 2, 5, 3], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_7_3.2.2-d
7T6-7_7_3.3.1-a	$7$	7T6	$[7, 7, 3]$	$[[7], [7], [3, 3, 1]]$	$2$	$1$	$\Q$	$[[[5, 6, 4, 2, 3, 7, 1], [5, 7, 4, 2, 3, 1, 6], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_7_3.3.1-a
7T6-7_7_3.3.1-b	$7$	7T6	$[7, 7, 3]$	$[[7], [7], [3, 3, 1]]$	$2$	$2$	$\Q(\sqrt{5}) $	$[[[2, 4, 5, 3, 6, 7, 1], [4, 7, 1, 5, 2, 3, 6], [2, 3, 1, 5, 6, 4, 7]], [[7, 3, 4, 5, 1, 2, 6], [2, 5, 6, 7, 3, 4, 1], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_7_3.3.1-b
7T6-7_7_3.3.1-c	$7$	7T6	$[7, 7, 3]$	$[[7], [7], [3, 3, 1]]$	$2$	$5$	5.1.46305.1	$[[[2, 3, 4, 5, 6, 7, 1], [2, 7, 1, 5, 3, 4, 6], [2, 3, 1, 5, 6, 4, 7]], [[6, 3, 4, 5, 1, 7, 2], [2, 5, 7, 1, 3, 4, 6], [2, 3, 1, 5, 6, 4, 7]], [[4, 3, 5, 2, 6, 7, 1], [2, 7, 4, 5, 1, 3, 6], [2, 3, 1, 5, 6, 4, 7]], [[6, 5, 4, 1, 3, 7, 2], [5, 4, 7, 1, 3, 2, 6], [2, 3, 1, 5, 6, 4, 7]], [[4, 6, 5, 3, 2, 7, 1], [4, 7, 5, 2, 1, 3, 6], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_7_3.3.1-c
7T7-7_4.3_4.3-a	$7$	7T7	$[7, 12, 12]$	$[[7], [4, 3], [4, 3]]$	$2$	$1$	$\Q$	$[[[2, 3, 4, 5, 6, 7, 1], [4, 5, 1, 7, 6, 2, 3], [4, 3, 6, 7, 1, 2, 5]]]$	7T7-7_4.3_4.3-a
7T7-7_4.3_4.3-b	$7$	7T7	$[7, 12, 12]$	$[[7], [4, 3], [4, 3]]$	$2$	$2$	$\Q(\sqrt{7}) $	$[[[2, 3, 4, 5, 6, 7, 1], [6, 3, 4, 2, 1, 7, 5], [6, 5, 4, 2, 3, 7, 1]], [[2, 3, 4, 5, 6, 7, 1], [4, 3, 7, 6, 2, 1, 5], [3, 6, 5, 2, 1, 7, 4]]]$	7T7-7_4.3_4.3-b
7T7-7_4.3_4.3-c	$7$	7T7	$[7, 12, 12]$	$[[7], [4, 3], [4, 3]]$	$2$	$2$	$\Q(\sqrt{-1}) $	$[[[2, 3, 4, 5, 6, 7, 1], [4, 6, 1, 5, 3, 7, 2], [6, 3, 7, 5, 1, 4, 2]], [[2, 3, 4, 5, 6, 7, 1], [4, 7, 5, 2, 6, 3, 1], [2, 7, 4, 6, 1, 3, 5]]]$	7T7-7_4.3_4.3-c
7T7-7_4.3_4.3-d	$7$	7T7	$[7, 12, 12]$	$[[7], [4, 3], [4, 3]]$	$2$	$4$	4.0.3024.2	$[[[2, 3, 4, 5, 6, 7, 1], [3, 6, 4, 5, 1, 7, 2], [6, 5, 7, 1, 3, 4, 2]], [[2, 3, 4, 5, 6, 7, 1], [4, 3, 7, 5, 6, 1, 2], [3, 6, 7, 2, 1, 4, 5]], [[2, 3, 4, 5, 6, 7, 1], [5, 6, 1, 7, 3, 4, 2], [4, 3, 7, 5, 6, 1, 2]], [[2, 3, 4, 5, 6, 7, 1], [4, 6, 7, 2, 3, 1, 5], [3, 6, 4, 5, 1, 7, 2]]]$	7T7-7_4.3_4.3-d

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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
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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.