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

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$D_{12}$
Group identifier:	$[24,6]$
Signature:	$[ 0; 2, 2, 2, 2, 12 ]$

Conjugacy classes for this refined passport:

$3, 4, 4, 4, 8$

Jacobian variety group algebra decomposition:	$E\times E\times E^{2}\times E^{2}\times E^{2}\times A_{2}^{2}$
Corresponding character(s):	$2, 3, 5, 6, 7, 8$

Other Data

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

Generating vector(s)

Displaying 20 of 36 generating vectors for this refined passport.

12.24-6.0.2-2-2-2-12.5.1

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.2

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,24) (2,23) (3,22) (4,21) (5,20) (6,19) (7,18) (8,17) (9,16) (10,15) (11,14) (12,13)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.3

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.4

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,23) (2,22) (3,24) (4,20) (5,19) (6,21) (7,17) (8,16) (9,18) (10,14) (11,13) (12,15)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.5

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.6

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
	(1,22) (2,24) (3,23) (4,19) (5,21) (6,20) (7,16) (8,18) (9,17) (10,13) (11,15) (12,14)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.7

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,22) (2,24) (3,23) (4,19) (5,21) (6,20) (7,16) (8,18) (9,17) (10,13) (11,15) (12,14)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.8

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,22) (2,24) (3,23) (4,19) (5,21) (6,20) (7,16) (8,18) (9,17) (10,13) (11,15) (12,14)
	(1,23) (2,22) (3,24) (4,20) (5,19) (6,21) (7,17) (8,16) (9,18) (10,14) (11,13) (12,15)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.9

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,24) (2,23) (3,22) (4,21) (5,20) (6,19) (7,18) (8,17) (9,16) (10,15) (11,14) (12,13)
	(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.10

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,24) (2,23) (3,22) (4,21) (5,20) (6,19) (7,18) (8,17) (9,16) (10,15) (11,14) (12,13)
	(1,22) (2,24) (3,23) (4,19) (5,21) (6,20) (7,16) (8,18) (9,17) (10,13) (11,15) (12,14)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.11

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,23) (2,22) (3,24) (4,20) (5,19) (6,21) (7,17) (8,16) (9,18) (10,14) (11,13) (12,15)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.12

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,23) (2,22) (3,24) (4,20) (5,19) (6,21) (7,17) (8,16) (9,18) (10,14) (11,13) (12,15)
	(1,24) (2,23) (3,22) (4,21) (5,20) (6,19) (7,18) (8,17) (9,16) (10,15) (11,14) (12,13)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.13

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.14

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,22) (2,24) (3,23) (4,19) (5,21) (6,20) (7,16) (8,18) (9,17) (10,13) (11,15) (12,14)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.15

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.16

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,24) (2,23) (3,22) (4,21) (5,20) (6,19) (7,18) (8,17) (9,16) (10,15) (11,14) (12,13)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.17

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

12.24-6.0.2-2-2-2-12.5.18

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,20) (2,19) (3,21) (4,23) (5,22) (6,24) (7,14) (8,13) (9,15) (10,17) (11,16) (12,18)
	(1,23) (2,22) (3,24) (4,20) (5,19) (6,21) (7,17) (8,16) (9,18) (10,14) (11,13) (12,15)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.19

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,22) (2,24) (3,23) (4,19) (5,21) (6,20) (7,16) (8,18) (9,17) (10,13) (11,15) (12,14)
	(1,19) (2,21) (3,20) (4,22) (5,24) (6,23) (7,13) (8,15) (9,14) (10,16) (11,18) (12,17)
	(1,8,6,10,2,9,4,11,3,7,5,12) (13,20,18,22,14,21,16,23,15,19,17,24)

12.24-6.0.2-2-2-2-12.5.20

	(1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20)
	(1,21) (2,20) (3,19) (4,24) (5,23) (6,22) (7,15) (8,14) (9,13) (10,18) (11,17) (12,16)
	(1,22) (2,24) (3,23) (4,19) (5,21) (6,20) (7,16) (8,18) (9,17) (10,13) (11,15) (12,14)
	(1,24) (2,23) (3,22) (4,21) (5,20) (6,19) (7,18) (8,17) (9,16) (10,15) (11,14) (12,13)
	(1,12,5,7,3,11,4,9,2,10,6,8) (13,24,17,19,15,23,16,21,14,22,18,20)

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 $\F_{q}$

Label	12.24-6.0.2-2-2-2-12.5
Genus	\(12\)
Quotient genus	\(0\)
Group	\(D_{12}\)
Signature	\([ 0; 2, 2, 2, 2, 12 ]\)
Generating Vectors	\(36\)

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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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