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

Family Information

Genus:	$10$
Quotient genus:	$0$
Group name:	$D_{10}$
Group identifier:	$[20,4]$
Signature:	$[ 0; 2, 2, 2, 2, 10 ]$

Conjugacy classes for this refined passport:

$3, 3, 3, 4, 8$

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

Other Data

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

Generating vector(s)

Displaying 20 of 25 generating vectors for this refined passport.

10.20-4.0.2-2-2-2-10.4.1

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,18) (2,17) (3,16) (4,20) (5,19) (6,13) (7,12) (8,11) (9,15) (10,14)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.2

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,16) (2,20) (3,19) (4,18) (5,17) (6,11) (7,15) (8,14) (9,13) (10,12)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.3

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,20) (2,19) (3,18) (4,17) (5,16) (6,15) (7,14) (8,13) (9,12) (10,11)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.4

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,18) (2,17) (3,16) (4,20) (5,19) (6,13) (7,12) (8,11) (9,15) (10,14)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.5

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,17) (2,16) (3,20) (4,19) (5,18) (6,12) (7,11) (8,15) (9,14) (10,13)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.6

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,16) (2,20) (3,19) (4,18) (5,17) (6,11) (7,15) (8,14) (9,13) (10,12)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.7

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,17) (2,16) (3,20) (4,19) (5,18) (6,12) (7,11) (8,15) (9,14) (10,13)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.8

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,18) (2,17) (3,16) (4,20) (5,19) (6,13) (7,12) (8,11) (9,15) (10,14)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.9

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,19) (2,18) (3,17) (4,16) (5,20) (6,14) (7,13) (8,12) (9,11) (10,15)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.10

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,16) (2,20) (3,19) (4,18) (5,17) (6,11) (7,15) (8,14) (9,13) (10,12)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.11

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,20) (2,19) (3,18) (4,17) (5,16) (6,15) (7,14) (8,13) (9,12) (10,11)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.12

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,12) (2,11) (3,15) (4,14) (5,13) (6,17) (7,16) (8,20) (9,19) (10,18)
	(1,18) (2,17) (3,16) (4,20) (5,19) (6,13) (7,12) (8,11) (9,15) (10,14)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.13

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,12) (2,11) (3,15) (4,14) (5,13) (6,17) (7,16) (8,20) (9,19) (10,18)
	(1,17) (2,16) (3,20) (4,19) (5,18) (6,12) (7,11) (8,15) (9,14) (10,13)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.14

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,14) (2,13) (3,12) (4,11) (5,15) (6,19) (7,18) (8,17) (9,16) (10,20)
	(1,20) (2,19) (3,18) (4,17) (5,16) (6,15) (7,14) (8,13) (9,12) (10,11)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.15

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,14) (2,13) (3,12) (4,11) (5,15) (6,19) (7,18) (8,17) (9,16) (10,20)
	(1,19) (2,18) (3,17) (4,16) (5,20) (6,14) (7,13) (8,12) (9,11) (10,15)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.16

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,20) (2,19) (3,18) (4,17) (5,16) (6,15) (7,14) (8,13) (9,12) (10,11)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.17

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,19) (2,18) (3,17) (4,16) (5,20) (6,14) (7,13) (8,12) (9,11) (10,15)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.18

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,16) (2,20) (3,19) (4,18) (5,17) (6,11) (7,15) (8,14) (9,13) (10,12)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

10.20-4.0.2-2-2-2-10.4.19

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,13) (2,12) (3,11) (4,15) (5,14) (6,18) (7,17) (8,16) (9,20) (10,19)
	(1,17) (2,16) (3,20) (4,19) (5,18) (6,12) (7,11) (8,15) (9,14) (10,13)
	(1,8,5,7,4,6,3,10,2,9) (11,18,15,17,14,16,13,20,12,19)

10.20-4.0.2-2-2-2-10.4.20

	(1,11) (2,15) (3,14) (4,13) (5,12) (6,16) (7,20) (8,19) (9,18) (10,17)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,15) (2,14) (3,13) (4,12) (5,11) (6,20) (7,19) (8,18) (9,17) (10,16)
	(1,18) (2,17) (3,16) (4,20) (5,19) (6,13) (7,12) (8,11) (9,15) (10,14)
	(1,9,2,10,3,6,4,7,5,8) (11,19,12,20,13,16,14,17,15,18)

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	10.20-4.0.2-2-2-2-10.4
Genus	\(10\)
Quotient genus	\(0\)
Group	\(D_{10}\)
Signature	\([ 0; 2, 2, 2, 2, 10 ]\)
Generating Vectors	\(25\)

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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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