LMFDB - One refined passport of genus 10 with automorphism group $A

Family Information

Genus:	$10$
Quotient genus:	$0$
Group name:	$A_4$
Group identifier:	$[12,3]$
Signature:	$[ 0; 2, 2, 2, 3, 3, 3 ]$

Conjugacy classes for this refined passport:

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

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

Other Data

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

Generating vector(s)

Displaying 20 of 36 generating vectors for this refined passport.

10.12-3.0.2-2-2-3-3-3.1.1

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

10.12-3.0.2-2-2-3-3-3.1.2

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

10.12-3.0.2-2-2-3-3-3.1.3

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

10.12-3.0.2-2-2-3-3-3.1.4

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

10.12-3.0.2-2-2-3-3-3.1.5

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

10.12-3.0.2-2-2-3-3-3.1.6

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

10.12-3.0.2-2-2-3-3-3.1.7

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

10.12-3.0.2-2-2-3-3-3.1.8

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

10.12-3.0.2-2-2-3-3-3.1.9

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

10.12-3.0.2-2-2-3-3-3.1.10

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

10.12-3.0.2-2-2-3-3-3.1.11

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

10.12-3.0.2-2-2-3-3-3.1.12

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

10.12-3.0.2-2-2-3-3-3.1.13

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

10.12-3.0.2-2-2-3-3-3.1.14

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

10.12-3.0.2-2-2-3-3-3.1.15

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

10.12-3.0.2-2-2-3-3-3.1.16

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

10.12-3.0.2-2-2-3-3-3.1.17

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

10.12-3.0.2-2-2-3-3-3.1.18

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

10.12-3.0.2-2-2-3-3-3.1.19

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

10.12-3.0.2-2-2-3-3-3.1.20

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

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	10.12-3.0.2-2-2-3-3-3.1
Genus	\(10\)
Quotient genus	\(0\)
Group	\(A_4\)
Signature	\([ 0; 2, 2, 2, 3, 3, 3 ]\)
Generating Vectors	\(36\)

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Other Data

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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