X(68095) = (name pending)
Barycentrics -2*a^12 - 5*a^10*(b^2 + c^2) + 11*a^8*(b^2 + c^2)^2 + 7*(b^2 - c^2)^4*(b^2 + c^2)^2 - a^2*(b^2 - c^2)^2*(5*b^6 - 13*b^4*c^2 - 13*b^2*c^4 + 5*c^6) + 2*a^6*(5*b^6 - 9*b^4*c^2 - 9*b^2*c^4 + 5*c^6) - 8*a^4*(2*b^8 + b^6*c^2 - 4*b^4*c^4 + b^2*c^6 + 2*c^8) : :As a point on the Euler line, X(68095) has Shinagawa coefficients: {-13 e (e + f) + 5 (e + f)^2 + 120 R^4, (e + f) (-8 e + 9 (e + f))}
See David Nguyen, euclid 8214.
X(68095) lies on this line: {2, 3}
X(68096) = EULER LINE INTERCEPT OF X(13562)X(47447)
Barycentrics 10*a^12 - 11*a^10*(b^2 + c^2) + (b^2 - c^2)^4*(b^2 + c^2)^2 + a^8*(-19*b^4 + 18*b^2*c^2 - 19*c^4) + 2*a^6*(11*b^6 - 7*b^4*c^2 - 7*b^2*c^4 + 11*c^6) - a^2*(b^2 - c^2)^2*(11*b^6 - 3*b^4*c^2 - 3*b^2*c^4 + 11*c^6) + 8*a^4*(b^8 - 2*b^6*c^2 + 4*b^4*c^4 - 2*b^2*c^6 + c^8) : :As a point on the Euler line, X(68096) has Shinagawa coefficients: {1/3 (-54 e (e + f) + 33 (e + f)^2 + 360 R^4), (e + f) (7 e - 9 (e + f))}
See David Nguyen, euclid 8214.
X(68096) lies on these lines: {2, 3}, {13562, 47447}
X(68097) = (name pending)
Barycentrics 10*a^18 - 57*a^16*(b^2 + c^2) + 37*(b^2 - c^2)^6*(b^2 + c^2)^3 + 6*a^14*(9*b^4 + 46*b^2*c^2 + 9*c^4) - 4*a^2*(b^2 - c^2)^4*(b^2 + c^2)^2*(21*b^4 - 34*b^2*c^2 + 21*c^4) + 2*a^12*(67*b^6 - 149*b^4*c^2 - 149*b^2*c^4 + 67*c^6) - 2*a^10*(111*b^8 + 124*b^6*c^2 - 318*b^4*c^4 + 124*b^2*c^6 + 111*c^8) - 4*a^8*(15*b^10 - 164*b^8*c^2 + 121*b^6*c^4 + 121*b^4*c^6 - 164*b^2*c^8 + 15*c^10) - 2*a^4*(b^2 - c^2)^2*(27*b^10 + 149*b^8*c^2 - 120*b^6*c^4 - 120*b^4*c^6 + 149*b^2*c^8 + 27*c^10) + 2*a^6*(121*b^12 - 166*b^10*c^2 - 209*b^8*c^4 + 572*b^6*c^6 - 209*b^4*c^8 - 166*b^2*c^10 + 121*c^12) : :As a point on the Euler line, X(68097) has Shinagawa coefficients: {1/3 (-429 e (e + f)^2 + 141 (e + f)^3 + 6744 (e + f) R^4 - 8640 R^6), (e + f) (-44 e (e + f) + 27 (e + f)^2 + 288 R^4)}
See David Nguyen, euclid 8214.
X(68097) lies on this line: {2, 3}
X(68098) = (name pending)
Barycentrics (a^2 - b^2 - c^2)*(4*a^26 - 17*a^24*(b^2 + c^2) - (b^2 - c^2)^10*(b^2 + c^2)^3 + 8*a^2*(b^2 - c^2)^8*(b^2 + c^2)^2*(b^4 + 6*b^2*c^2 + c^4) + 2*a^22*(6*b^4 - 23*b^2*c^2 + 6*c^4) + a^20*(46*b^6 + 312*b^4*c^2 + 312*b^2*c^4 + 46*c^6) - 16*a^18*(5*b^8 + 12*b^6*c^2 + 45*b^4*c^4 + 12*b^2*c^6 + 5*c^8) - 2*a^4*(b^2 - c^2)^6*(9*b^10 + 134*b^8*c^2 + 277*b^6*c^4 + 277*b^4*c^6 + 134*b^2*c^8 + 9*c^10) - a^16*(15*b^10 + 695*b^8*c^2 - 126*b^6*c^4 - 126*b^4*c^6 + 695*b^2*c^8 + 15*c^10) - 2*a^6*(b^2 - c^2)^4*(2*b^12 - 157*b^10*c^2 - 350*b^8*c^4 - 478*b^6*c^6 - 350*b^4*c^8 - 157*b^2*c^10 + 2*c^12) + 4*a^14*(30*b^12 + 213*b^10*c^2 + 118*b^8*c^4 - 234*b^6*c^6 + 118*b^4*c^8 + 213*b^2*c^10 + 30*c^12) - 4*a^12*(15*b^14 - 94*b^12*c^2 + 110*b^10*c^4 - 287*b^8*c^6 - 287*b^6*c^8 + 110*b^4*c^10 - 94*b^2*c^12 + 15*c^14) + a^8*(b^2 - c^2)^2*(65*b^14 + 307*b^12*c^2 - 215*b^10*c^4 - 1181*b^8*c^6 - 1181*b^6*c^8 - 215*b^4*c^10 + 307*b^2*c^12 + 65*c^14) + a^10*(-60*b^16 - 944*b^14*c^2 + 992*b^12*c^4 + 560*b^10*c^6 - 584*b^8*c^8 + 560*b^6*c^10 + 992*b^4*c^12 - 944*b^2*c^14 - 60*c^16)) : :As a point on the Euler line, X(68098) has Shinagawa coefficients: {-((-(e/4) - f) (11/2 e (e + f)^2 + 5 (e + f)^3 - 320 (e + f) R^4 + 640 R^6)), (2 e - 3 (e + f)) (1/4 e (e + f)^2 + (e + f)^3 - 38 (e + f) R^4 + 80 R^6)}
See David Nguyen, euclid 8221.
X(68098) lies on this line: {2, 3}
X(68099) = (name pending)
Barycentrics 92*a^28 - 483*a^26*(b^2 + c^2) + 23*(b^2 - c^2)^10*(b^2 + c^2)^4 - a^2*(b^2 - c^2)^8*(b^2 + c^2)^3*(207*b^4 + 112*b^2*c^2 + 207*c^4) + a^24*(667*b^4 + 1888*b^2*c^2 + 667*c^4) + 2*a^22*(391*b^6 - 822*b^4*c^2 - 822*b^2*c^4 + 391*c^6) + 2*a^4*(b^2 - c^2)^6*(b^2 + c^2)^2*(299*b^8 + 269*b^6*c^2 + 532*b^4*c^4 + 269*b^2*c^6 + 299*c^8) - 2*a^20*(1449*b^8 + 1187*b^6*c^2 - 656*b^4*c^4 + 1187*b^2*c^6 + 1449*c^8) + a^18*(1495*b^10 + 4745*b^8*c^2 - 1496*b^6*c^4 - 1496*b^4*c^6 + 4745*b^2*c^8 + 1495*c^10) + 4*a^12*b^2*c^2*(329*b^12 - 1510*b^10*c^2 - 449*b^8*c^4 + 1084*b^6*c^6 - 449*b^4*c^8 - 1510*b^2*c^10 + 329*c^12) + a^16*(3105*b^12 - 1938*b^10*c^2 + 623*b^8*c^4 + 7588*b^6*c^6 + 623*b^4*c^8 - 1938*b^2*c^10 + 3105*c^12) - 2*a^6*(b^2 - c^2)^4*(161*b^14 + 486*b^12*c^2 + 1432*b^10*c^4 + 2177*b^8*c^6 + 2177*b^6*c^8 + 1432*b^4*c^10 + 486*b^2*c^12 + 161*c^14) - 4*a^14*(1035*b^14 + 116*b^12*c^2 - 1206*b^10*c^4 + 903*b^8*c^6 + 903*b^6*c^8 - 1206*b^4*c^10 + 116*b^2*c^12 + 1035*c^14) - a^8*(b^2 - c^2)^2*(1587*b^16 + 74*b^14*c^2 - 3320*b^12*c^4 - 2378*b^10*c^6 - 1654*b^8*c^8 - 2378*b^6*c^10 - 3320*b^4*c^12 + 74*b^2*c^14 + 1587*c^16) + a^10*(2875*b^18 - 3393*b^16*c^2 + 320*b^14*c^4 + 2552*b^12*c^6 - 3378*b^10*c^8 - 3378*b^8*c^10 + 2552*b^6*c^12 + 320*b^4*c^14 - 3393*b^2*c^16 + 2875*c^18) : :As a point on the Euler line, X(68099) has Shinagawa coefficients: {-(697/2) e (e + f)^3 + 115 (e + f)^4 + 6268 (e + f)^2 R^4 - 12352 (e + f) R^6 + 8960 R^8, -((2 e - 3 (e + f)) (45 e (e + f)^2 - 23 (e + f)^3 - 440 (e + f) R^4 + 320 R^6))}
See David Nguyen, euclid 8221.
X(68099) lies on this line: {2, 3}
X(68100) = (name pending)
Barycentrics 10*a^24 - 31*a^22*(b^2 + c^2) + (b^2 - c^2)^8*(b^2 + c^2)^4 - 7*a^20*(b^4 - 16*b^2*c^2 + c^4) - a^2*(b^2 - c^2)^6*(b^2 + c^2)^3*(13*b^4 + 19*b^2*c^2 + 13*c^4) + a^18*(111*b^6 - 50*b^4*c^2 - 50*b^2*c^4 + 111*c^6) + a^4*(b^2 - c^2)^4*(b^2 + c^2)^2*(29*b^8 - 8*b^6*c^2 + 6*b^4*c^4 - 8*b^2*c^6 + 29*c^8) - a^16*(71*b^8 + 258*b^6*c^2 - 146*b^4*c^4 + 258*b^2*c^6 + 71*c^8) - 2*a^14*(67*b^10 - 158*b^8*c^2 + 9*b^6*c^4 + 9*b^4*c^6 - 158*b^2*c^8 + 67*c^10) + 2*a^12*(77*b^12 + 53*b^10*c^2 - 137*b^8*c^4 + 198*b^6*c^6 - 137*b^4*c^8 + 53*b^2*c^10 + 77*c^12) + a^6*(b^2 - c^2)^2*(21*b^14 + 125*b^12*c^2 + 23*b^10*c^4 - 57*b^8*c^6 - 57*b^6*c^8 + 23*b^4*c^10 + 125*b^2*c^12 + 21*c^14) + a^10*(46*b^14 - 338*b^12*c^2 + 230*b^10*c^4 - 50*b^8*c^6 - 50*b^6*c^8 + 230*b^4*c^10 - 338*b^2*c^12 + 46*c^14) - 2*a^8*(58*b^16 - 55*b^14*c^2 - 70*b^12*c^4 + 127*b^10*c^6 - 56*b^8*c^8 + 127*b^6*c^10 - 70*b^4*c^12 - 55*b^2*c^14 + 58*c^16) : :As a point on the Euler line, X(68100) has Shinagawa coefficients: {1/3 (-(819/4) e (e + f)^3 + 66 (e + f)^4 + 3516 (e + f)^2 R^4 - 5928 (e + f) R^6 + 2880 R^8), (e + f) (227/4 e (e + f)^2 - 18 (e + f)^3 - 912 (e + f) R^4 + 1184 R^6)}
See David Nguyen, euclid 8221.
X(68100) lies on this line: {2, 3}
X(68101) = (name pending)
Barycentrics 10*a^30 - 41*a^28*(b^2 + c^2) + (b^2 - c^2)^10*(b^2 + c^2)^5 + 2*a^26*(7*b^4 + 61*b^2*c^2 + 7*c^4) - a^2*(b^2 - c^2)^8*(b^2 + c^2)^4*(14*b^4 + 53*b^2*c^2 + 14*c^4) + a^24*(159*b^6 + 56*b^4*c^2 + 56*b^2*c^4 + 159*c^6) + a^4*(b^2 - c^2)^6*(b^2 + c^2)^3*(41*b^8 + 165*b^6*c^2 - 120*b^4*c^4 + 165*b^2*c^6 + 41*c^8) - a^22*(206*b^8 + 481*b^6*c^2 + 446*b^4*c^4 + 481*b^2*c^6 + 206*c^8) + a^20*(-181*b^10 + 208*b^8*c^2 + 661*b^6*c^4 + 661*b^4*c^6 + 208*b^2*c^8 - 181*c^10) + a^6*(b^2 - c^2)^4*(b^2 + c^2)^2*(6*b^12 + 7*b^10*c^2 + 430*b^8*c^4 - 966*b^6*c^6 + 430*b^4*c^8 + 7*b^2*c^10 + 6*c^12) + a^18*(470*b^12 + 707*b^10*c^2 + 334*b^8*c^4 - 942*b^6*c^6 + 334*b^4*c^8 + 707*b^2*c^10 + 470*c^12) - a^16*(45*b^14 + 577*b^12*c^2 + 1719*b^10*c^4 - 1013*b^8*c^6 - 1013*b^6*c^8 + 1719*b^4*c^10 + 577*b^2*c^12 + 45*c^14) - 2*a^14*(225*b^16 + 229*b^14*c^2 - 682*b^12*c^4 - 541*b^10*c^6 + 2114*b^8*c^8 - 541*b^6*c^10 - 682*b^4*c^12 + 229*b^2*c^14 + 225*c^16) - a^8*(b^2 - c^2)^2*(179*b^18 + 584*b^16*c^2 + 3*b^14*c^4 - 1639*b^12*c^6 + 1449*b^10*c^8 + 1449*b^8*c^10 - 1639*b^6*c^12 + 3*b^4*c^14 + 584*b^2*c^16 + 179*c^18) + a^12*(245*b^18 + 543*b^16*c^2 + 626*b^14*c^4 - 3762*b^12*c^6 + 2924*b^10*c^8 + 2924*b^8*c^10 - 3762*b^6*c^12 + 626*b^4*c^14 + 543*b^2*c^16 + 245*c^18) + 2*a^10*(85*b^20 + 56*b^18*c^2 - 923*b^16*c^4 + 1184*b^14*c^6 + 1286*b^12*c^8 - 3120*b^10*c^10 + 1286*b^8*c^12 + 1184*b^6*c^14 - 923*b^4*c^16 + 56*b^2*c^18 + 85*c^20) : :As a point on the Euler line, X(68101) has Shinagawa coefficients: {-(253/4) e (e + f)^4 + 22 (e + f)^5 + 774 (e + f)^3 R^4 + 880 (e + f)^2 R^6 - 7760 (e + f) R^8 + 9600 R^10, -((e + f) (-(263/4) e (e + f)^3 + 18 (e + f)^4 + 1382 (e + f)^2 R^4 - 3120 (e + f) R^6 + 2560 R^8))}
See David Nguyen, euclid 8221.
X(68101) lies on this line: {2, 3}