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

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$A_4$
Group identifier:	$[12,3]$
Signature:	$[ 0; 2, 3, 3, 3, 3, 3 ]$

Conjugacy classes for this refined passport:

$2, 3, 4, 4, 4, 4$

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

Other Data

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

Generating vector(s)

Displaying 20 of 64 generating vectors for this refined passport.

12.12-3.0.2-3-3-3-3-3.2.1

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

12.12-3.0.2-3-3-3-3-3.2.2

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

12.12-3.0.2-3-3-3-3-3.2.3

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

12.12-3.0.2-3-3-3-3-3.2.4

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

12.12-3.0.2-3-3-3-3-3.2.5

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

12.12-3.0.2-3-3-3-3-3.2.6

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

12.12-3.0.2-3-3-3-3-3.2.7

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

12.12-3.0.2-3-3-3-3-3.2.8

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

12.12-3.0.2-3-3-3-3-3.2.9

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

12.12-3.0.2-3-3-3-3-3.2.10

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

12.12-3.0.2-3-3-3-3-3.2.11

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

12.12-3.0.2-3-3-3-3-3.2.12

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

12.12-3.0.2-3-3-3-3-3.2.13

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

12.12-3.0.2-3-3-3-3-3.2.14

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

12.12-3.0.2-3-3-3-3-3.2.15

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

12.12-3.0.2-3-3-3-3-3.2.16

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

12.12-3.0.2-3-3-3-3-3.2.17

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

12.12-3.0.2-3-3-3-3-3.2.18

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

12.12-3.0.2-3-3-3-3-3.2.19

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

12.12-3.0.2-3-3-3-3-3.2.20

	(1,2) (3,4) (5,6) (7,8) (9,10) (11,12)
	(1,5,9) (2,8,11) (3,6,12) (4,7,10)
	(1,12,7) (2,10,6) (3,9,8) (4,11,5)
	(1,9,5) (2,11,8) (3,12,6) (4,10,7)
	(1,11,6) (2,9,7) (3,10,5) (4,12,8)
	(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 $\F_{q}$

Label	12.12-3.0.2-3-3-3-3-3.2
Genus	\(12\)
Quotient genus	\(0\)
Group	\(A_4\)
Signature	\([ 0; 2, 3, 3, 3, 3, 3 ]\)
Generating Vectors	\(64\)

Introduction

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Family Information

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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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