LMFDB - One refined passport of genus 7 with automorphism group $D

Family Information

Genus:	$7$
Quotient genus:	$0$
Group name:	$D_6$
Group identifier:	$[12,4]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2 ]$

Conjugacy classes for this refined passport:

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

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

Other Data

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

Generating vector(s)

Displaying 20 of 40 generating vectors for this refined passport.

7.12-4.0.2-2-2-2-2-2.4.1

	(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)
	(1,7) (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)

7.12-4.0.2-2-2-2-2-2.4.2

	(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)
	(1,9) (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)

7.12-4.0.2-2-2-2-2-2.4.3

	(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)
	(1,9) (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)

7.12-4.0.2-2-2-2-2-2.4.4

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

7.12-4.0.2-2-2-2-2-2.4.5

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

7.12-4.0.2-2-2-2-2-2.4.6

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

7.12-4.0.2-2-2-2-2-2.4.7

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

7.12-4.0.2-2-2-2-2-2.4.8

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

7.12-4.0.2-2-2-2-2-2.4.9

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

7.12-4.0.2-2-2-2-2-2.4.10

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

7.12-4.0.2-2-2-2-2-2.4.11

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

7.12-4.0.2-2-2-2-2-2.4.12

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

7.12-4.0.2-2-2-2-2-2.4.13

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

7.12-4.0.2-2-2-2-2-2.4.14

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

7.12-4.0.2-2-2-2-2-2.4.15

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

7.12-4.0.2-2-2-2-2-2.4.16

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

7.12-4.0.2-2-2-2-2-2.4.17

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

7.12-4.0.2-2-2-2-2-2.4.18

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

7.12-4.0.2-2-2-2-2-2.4.19

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

7.12-4.0.2-2-2-2-2-2.4.20

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

Displaying the unique representative of this refined passport up to braid equivalence.

7.12-4.0.2-2-2-2-2-2.4.1

	(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)
	(1,7) (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)

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	7.12-4.0.2-2-2-2-2-2.4
Genus	\(7\)
Quotient genus	\(0\)
Group	\(D_6\)
Signature	\([ 0; 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors	\(40\)

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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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