Q(rt2)
Disc=8
--------------------
n=4

Gram Matrix
A=

[2,1,rt2,rt2]
[1,2,rt2,rt2]
[rt2,rt2,2,1]
[rt2,rt2,1,2]

h=1

Automorphism group size:
[2304]

Trivial case.

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

Gram Matrix
A oplus A

h=6

Automorphism group sizes:
[10616832,10321920,786432,696729600,442368,5160960]

Neighbour Matrices:

N(P)=2

[18,36,81,0,0,0]
[35,28,0,2,70,0]
[6,0,49,0,64,16]
[0,135,0,0,0,0]
[0,3,36,0,96,0]
[0,0,105,0,0,30]

CharPoly = (x-135)*(x-58)*(x+8)*(x+30)*(x^2-66x+432)

N(P)=9

[36936,27648,152064,1024,362496,18432]
[26880,51016,161280,1024,358400,0]
[11264,12288,208456,0,333824,32768]
[67200,69120,0,8680,453600,0]
[15104,15360,187776,288,352424,27648]
[8960,0,215040,0,322560,52040]

CharPoly = (x-598600)*(x-66376)*(x-21320)*(x-3016)*(x^2-20240*x+94939200)

N(P)=7

[7040,9216,41472,0,79872,0]
[8960,11648,26880,512,89600,0]
[3072,2048,46464,0,77824,8192]
[0,34560,0,2240 100800,0]
[3328,3840,43776,64,80448,6144]
[0,0,53760,0,71680,12160]

CharPoly = (x-137600)*(x-19328)*(x+384)*(x+3200)*(x^2-6656*x+9879552)

--------------------
n=12

Gram matrix
A oplus A oplus A

Mass = 8.54219494697261359957271012650

Too big.