LMFDB - One refined passport of genus 9 with automorphism group $A

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$A_4$
Group identifier:	$[12,3]$
Signature:	$[ 0; 3, 3, 3, 3, 3 ]$

Conjugacy classes for this refined passport:

$3, 3, 3, 3, 4$

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

Other Data

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

Generating vector(s)

Displaying 20 of 21 generating vectors for this refined passport.

9.12-3.0.3-3-3-3-3.1.1

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

9.12-3.0.3-3-3-3-3.1.2

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

9.12-3.0.3-3-3-3-3.1.3

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

9.12-3.0.3-3-3-3-3.1.4

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

9.12-3.0.3-3-3-3-3.1.5

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

9.12-3.0.3-3-3-3-3.1.6

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

9.12-3.0.3-3-3-3-3.1.7

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

9.12-3.0.3-3-3-3-3.1.8

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

9.12-3.0.3-3-3-3-3.1.9

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

9.12-3.0.3-3-3-3-3.1.10

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

9.12-3.0.3-3-3-3-3.1.11

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

9.12-3.0.3-3-3-3-3.1.12

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

9.12-3.0.3-3-3-3-3.1.13

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

9.12-3.0.3-3-3-3-3.1.14

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

9.12-3.0.3-3-3-3-3.1.15

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

9.12-3.0.3-3-3-3-3.1.16

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

9.12-3.0.3-3-3-3-3.1.17

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

9.12-3.0.3-3-3-3-3.1.18

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

9.12-3.0.3-3-3-3-3.1.19

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

9.12-3.0.3-3-3-3-3.1.20

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

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	9.12-3.0.3-3-3-3-3.1
Genus	\(9\)
Quotient genus	\(0\)
Group	\(A_4\)
Signature	\([ 0; 3, 3, 3, 3, 3 ]\)
Generating Vectors	\(21\)

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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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