Q(rt10)
Disc=40
--------------------
n=4

Gram Matrix 
A=
[2,1,-7*rt10-8,85*rt10-314]
[1,2,0,0]
[-7*rt10-8,0,78*rt10+454,1518*rt10-3749]
[85*rt10-314,0,1518*rt10-3749,-55488*rt10+177046]

h=6

Automorphism group sizes:
[1152, 128, 32, 96, 72, 48]

Neighbour Matrices:

N(P)=2

[0 9 0 0 0 0]
[1 0 4 4 0 0]
[0 1 0 0 4 4]
[0 3 0 0 0 6]
[0 0 9 0 0 0]
[0 0 6 3 0 0]

CharPoly = (x-9)(x-2)(x+2)(x+9)(x^2-18)

N(P)=3

[ 0  0  0  0 16  0]
[ 0  0 16  0  0  0]
[ 0  4  0  0  4  8]
[ 0  0  0  0  8  8]
[ 1  0  9  6  0  0]
[ 0  0 12  4  0  0]

CharPoly = (x-16)(x-2)(x+2)(x+16)(x^2-32)

N(P)=25

[ 0 36  0  0  0  0]
[ 4  0 16 16  0  0]
[ 0  4  0  0 16 16]
[ 0 12  0  0  0 24]
[ 0  0 36  0  0  0]
[ 0  0 24 12  0  0]

CharPoly = (x-36)(x-8)(x+8)(x+36)(x^2-288)

N(P)=49

[ 196    0 1296 1008    0    0]
[   0  676    0    0  576 1248]
[  36    0 1936  528    0    0]
[  84    0 1584  832    0    0]
[   0  324    0    0 1024 1152]
[   0  468    0    0  768 1264]

CharPoly = (x-2500)^2(x-400)^2(x-64)^2

--------------------
n=8

Gram Matrix
A oplus A

Mass = 31602.5

Too big.