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:

$3, 4, 4, 4, 7$

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

Other Data

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

Generating vector(s)

Displaying 20 of 25 generating vectors for this refined passport.

10.20-4.0.2-2-2-2-10.5.1

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

10.20-4.0.2-2-2-2-10.5.2

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

10.20-4.0.2-2-2-2-10.5.3

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

10.20-4.0.2-2-2-2-10.5.4

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

10.20-4.0.2-2-2-2-10.5.5

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

10.20-4.0.2-2-2-2-10.5.6

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

10.20-4.0.2-2-2-2-10.5.7

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

10.20-4.0.2-2-2-2-10.5.8

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

10.20-4.0.2-2-2-2-10.5.9

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

10.20-4.0.2-2-2-2-10.5.10

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

10.20-4.0.2-2-2-2-10.5.11

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

10.20-4.0.2-2-2-2-10.5.12

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

10.20-4.0.2-2-2-2-10.5.13

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

10.20-4.0.2-2-2-2-10.5.14

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

10.20-4.0.2-2-2-2-10.5.15

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

10.20-4.0.2-2-2-2-10.5.16

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

10.20-4.0.2-2-2-2-10.5.17

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

10.20-4.0.2-2-2-2-10.5.18

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

10.20-4.0.2-2-2-2-10.5.19

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

10.20-4.0.2-2-2-2-10.5.20

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

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	10.20-4.0.2-2-2-2-10.5
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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