Sato-Tate Distributions of twists of y2 = x8 - 14x4 + 1
Curve 1. x4+y4+z4 = 0, -2t2 = x4 + y4 + z4
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 2. y2 = x8 - 56x4 + 16
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 3. y2 = -x8 - 14x4 - 1
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 4. y2 = -x8 - x7 - 7x6 - 7x5 - 7x3 - 7x2 +x - 1
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 5. y2 = -x8 - 56x4 - 16
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 6. y2 = x8 - 14x4 + 1
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 7. y2 = x8 - 2x7 - 14x6 + 14x5 - 14x4 + 14x3 - 14x2 + 2x + 1
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 8. x2 + y2 + z2 = 0, 6t2 = -23x4 - 16x3y - 12x2y2 + 20xy3 - 23y4 - 20x3z - 12x2yz + 12xy2z - 16y3z - 12x2z2 - 12xyz2 - 12y2z2 + 16xz3 + 20yz3 - 23z4
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 9. y2 = -6x7 + 21x4 + 12x
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 10. y2 = -x8 + 4x7 - 28x6 + 28x5 + 14x4 + 28x3 - 196x2 + 100x - 61
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
Curve 11. y2 = x8 - 14x7 + 84x6 - 294x5 + 651x4 - 882x3 + 630x2 - 126x - 54
a1: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
M[a1] = (1, ...)
M[a2] = (1, ...)
M[a3] = (1, ...)
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
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s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
s3: 
s4: 
s5: 
s6: 
s7: 
a2: 
a3: 
s2: 
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s4: 
s5: 
s6: 
s7: 