LMFDB - One refined passport of genus 15 with automorphism group $\SD

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$\SD_{16}$
Group identifier:	$[16,8]$
Signature:	$[ 0; 2, 2, 2, 2, 8, 8 ]$

Conjugacy classes for this refined passport:

$3, 3, 3, 3, 7, 7$

Jacobian variety group algebra decomposition:	$A_{2}\times E\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$3, 4, 5, 6$

Other Data

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

Generating vector(s)

Displaying 20 of 32 generating vectors for this refined passport.

15.16-8.0.2-2-2-2-8-8.6.1

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.2

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.3

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.4

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

15.16-8.0.2-2-2-2-8-8.6.5

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

15.16-8.0.2-2-2-2-8-8.6.6

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.7

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,8) (2,7) (3,6) (4,5) (9,16) (10,15) (11,14) (12,13)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.8

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,8) (2,7) (3,6) (4,5) (9,16) (10,15) (11,14) (12,13)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

15.16-8.0.2-2-2-2-8-8.6.9

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.10

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

15.16-8.0.2-2-2-2-8-8.6.11

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.12

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.13

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.14

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

15.16-8.0.2-2-2-2-8-8.6.15

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.16

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

15.16-8.0.2-2-2-2-8-8.6.17

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.18

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

15.16-8.0.2-2-2-2-8-8.6.19

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)

15.16-8.0.2-2-2-2-8-8.6.20

	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
	(1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
	(1,16,4,14,2,15,3,13) (5,10,8,11,6,9,7,12)
	(1,14,3,16,2,13,4,15) (5,11,7,10,6,12,8,9)

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	15.16-8.0.2-2-2-2-8-8.6
Genus	\(15\)
Quotient genus	\(0\)
Group	\(\SD_{16}\)
Signature	\([ 0; 2, 2, 2, 2, 8, 8 ]\)
Generating Vectors	\(32\)

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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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