Q(rt21)
Disc=21
--------------------
n=4

Gram Matrix 
A=
[2,1/2*(rt21-3),0,0]
[1/2*(rt21-3),-rt21+5,0,0]
[0,0,2,1/2*(rt21-3)]
[0,0,1/2*(rt21-3),-rt21+5]

h=3

Automorphism group sizes:
[288, 576, 576]

Neighbour Matrices:

N(P)=4

[25  0  0]
[ 0 17  8]
[ 0  8 17]

CharPoly = (x-25)^2(x-9)

N(P)=3

[ 0  8  8]
[16  0  0]
[16  0  0]

CharPoly = x(x-16)(x+16)

N(P)=25

[ 0 18 18]
[36  0  0]
[36  0  0]

CharPoly = x(x-36)(x+36)

N(P)=49

[64  0  0]
[ 0 32 32]
[ 0 32 32]

CharPoly = x(x-64)^2

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

Gram Matrix
A oplus A

Mass = 2.45

Too big.