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K1247

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X(2), X(3), X(4), X(6), X(9), X(32), X(57), X(83), X(238), X(985), X(987), X(3496), X(3500), X(5255), X(37652)

X(45983) → X(45987)

isogonal conjugate of X(37653)

see points below

Geometric properties :

See K1245 for explanations. See also Table 30.

K1247 is invariant under the involution M -> GM /\ KM* , where M* is the isogonal conjugate of M.

Points on K1247 :

Q1 = a (a b^2-b^3+a^2 c+a b c+b^2 c+a c^2) (a^4+a^3 b+a^2 b^2+a^3 c+a^2 c^2+b^2 c^2) (a^2 b+a b^2+a b c+a c^2+b c^2-c^3) : : , SEARCH = 0.4609255289408299

Q2 = b^2 c^2 (-a^7-a^6 b-a^5 b^2+a^3 b^4-a^6 c+a^3 b^3 c+a^2 b^4 c-a^5 c^2+a b^4 c^2+a^3 b c^3+a b^3 c^3+b^4 c^3+a^3 c^4+a^2 b c^4+a b^2 c^4+b^3 c^4) : : , SEARCH = 8.583394420515898

Q3 = a^2 (a^7+2 a^6 b+a^5 b^2-a^4 b^3-2 a^3 b^4-a^2 b^5+2 a^6 c+a^5 b c-a^3 b^3 c-2 a^2 b^4 c+a^5 c^2-a^2 b^3 c^2-2 a b^4 c^2-a^4 c^3-a^3 b c^3-a^2 b^2 c^3-2 a b^3 c^3-2 b^4 c^3-2 a^3 c^4-2 a^2 b c^4-2 a b^2 c^4-2 b^3 c^4-a^2 c^5) : : , SEARCH = -12.26155629138688

Q4 = a (a^3+b^3-a^2 c-a b c-b^2 c) (a^3+a^2 b-a b^2-b^3+a^2 c-2 a b c+b^2 c-a c^2+b c^2-c^3) (a^3-a^2 b-a b c-b c^2+c^3) : : , SEARCH = -1.583894331680611

Q5 = a (a+b-c) (a-b+c) (a^6+2 a^5 b-2 a^3 b^3-a^2 b^4+2 a^5 c-a^4 b c-2 a b^4 c+b^5 c+2 a^2 b^2 c^2-2 a b^3 c^2-2 a^3 c^3-2 a b^2 c^3-2 b^3 c^3-a^2 c^4-2 a b c^4+b c^5) : : , SEARCH = -0.5992926192548304

Q6 = a (-a^2 b^2+a^3 c+a^2 b c+a b^2 c+b^3 c) (a b^2-b^3+a b c+a c^2-c^3) (a^3 b+a^2 b c-a^2 c^2+a b c^2+b c^3) : : , SEARCH = -2.723204779684951

Q7 = (a^2+2 a b+b^2+c^2) (a^2+b^2+2 a c+c^2) (3 a^3+a^2 b-a b^2+b^3+a^2 c+b^2 c-a c^2+b c^2+c^3) : : , SEARCH = 1.745170926567628

Q8 = a^2 (a^3+2 a^2 b+2 a b^2+b^3+2 a^2 c+a b c+2 b^2 c-c^3) (a^3+2 a^2 b-b^3+2 a^2 c+a b c+2 a c^2+2 b c^2+c^3) : : , SEARCH = 0.4619781959327362

Q9 = (a^2+b^2-c^2) (a^2-b^2+c^2) (2 a^6+a^5 b-2 a^3 b^3-2 a^2 b^4+a b^5+a^5 c-a^4 b c-a b^4 c+b^5 c-2 a^3 c^3-2 b^3 c^3-2 a^2 c^4-a b c^4+a c^5+b c^5) : : , SEARCH = 0.4660956451869873

Q10 = a (a+b-c) (a-b+c) (b^2+a c) (a b+c^2) (a^5+a^2 b^3+a^2 b^2 c+a^2 b c^2-a b^2 c^2+b^3 c^2+a^2 c^3+b^2 c^3) : : , SEARCH = 0.3548737147309337