LMFDB - One refined passport of genus 12 with automorphism group $D

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$D_6$
Group identifier:	$[12,4]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 6 ]$

Conjugacy classes for this refined passport:

$3, 3, 3, 4, 4, 4, 6$

Jacobian variety group algebra decomposition:	$A_{2}\times E\times E\times A_{2}^{2}\times A_{2}^{2}$
Corresponding character(s):	$2, 3, 4, 5, 6$

Other Data

Hyperelliptic curve(s):	no
Cyclic trigonal curve(s):	no

Generating vector(s)

Displaying 20 of 81 generating vectors for this refined passport.

12.12-4.0.2-2-2-2-2-2-6.5.1

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.2

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.3

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.4

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.5

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.6

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.7

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.8

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.9

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.10

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.11

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.12

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.13

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.14

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.15

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.16

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.17

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.18

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,6,2,4,3,5) (7,12,8,10,9,11)

12.12-4.0.2-2-2-2-2-2-6.5.19

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

12.12-4.0.2-2-2-2-2-2-6.5.20

	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
	(1,11) (2,10) (3,12) (4,8) (5,7) (6,9)
	(1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
	(1,5,3,4,2,6) (7,11,9,10,8,12)

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Label	12.12-4.0.2-2-2-2-2-2-6.5
Genus	\(12\)
Quotient genus	\(0\)
Group	\(D_6\)
Signature	\([ 0; 2, 2, 2, 2, 2, 2, 6 ]\)
Generating Vectors	\(81\)

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Generating vector(s)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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