X(44299) = X(2)X(51)∩X(110)X(7484)
Barycentrics a^2*(a^2*b^2 - b^4 + a^2*c^2 - 7*b^2*c^2 - c^4) : :X(44299) = 9 X[2] - 2 X[51], 13 X[2] - 6 X[373], 6 X[2] + X[2979], 8 X[2] - X[3060], 3 X[2] + 4 X[3819], 5 X[2] + 2 X[3917], 10 X[2] - 3 X[5640], X[2] + 6 X[5650], 11 X[2] - 4 X[5943], 15 X[2] - 8 X[6688], 4 X[2] + 3 X[7998], 23 X[2] - 16 X[10219], 17 X[2] - 3 X[11002], 12 X[2] - 5 X[11451], 31 X[2] - 24 X[12045], 5 X[2] - 12 X[15082], 31 X[2] - 3 X[16981], 25 X[2] - 4 X[21849], 23 X[2] - 2 X[21969], 2 X[2] - 9 X[33879], 11 X[2] + 3 X[33884], 16 X[3] + 5 X[11439], 6 X[3] + X[11455], 17 X[3] + 4 X[32137], 13 X[51] - 27 X[373], 4 X[51] + 3 X[2979], 16 X[51] - 9 X[3060], X[51] + 6 X[3819], 5 X[51] + 9 X[3917], 20 X[51] - 27 X[5640], X[51] + 27 X[5650], 11 X[51] - 18 X[5943], 5 X[51] - 12 X[6688], 8 X[51] + 27 X[7998], 23 X[51] - 72 X[10219], 34 X[51] - 27 X[11002], 8 X[51] - 15 X[11451], 31 X[51] - 108 X[12045], 5 X[51] - 54 X[15082], 62 X[51] - 27 X[16981], 25 X[51] - 18 X[21849], 23 X[51] - 9 X[21969], 4 X[51] - 81 X[33879], 22 X[51] + 27 X[33884], 8 X[140] - X[5890], 16 X[140] + 5 X[11444], 20 X[140] + X[18436], 36 X[373] + 13 X[2979], 48 X[373] - 13 X[3060], 9 X[373] + 26 X[3819], 15 X[373] + 13 X[3917], 20 X[373] - 13 X[5640], X[373] + 13 X[5650], 33 X[373] - 26 X[5943], 45 X[373] - 52 X[6688], 8 X[373] + 13 X[7998], 69 X[373] - 104 X[10219], 34 X[373] - 13 X[11002], 72 X[373] - 65 X[11451], 31 X[373] - 52 X[12045], 5 X[373] - 26 X[15082], 62 X[373] - 13 X[16981], 75 X[373] - 26 X[21849], 69 X[373] - 13 X[21969], 4 X[373] - 39 X[33879], 22 X[373] + 13 X[33884], 8 X[549] - X[15072], 6 X[549] + X[18435], X[568] - 8 X[10124], 5 X[631] + 2 X[5891], 20 X[631] + X[12111], 10 X[631] - 3 X[20791], 25 X[631] - 4 X[40647], 20 X[632] + X[11412], 25 X[632] - 4 X[16881], 4 X[1216] + 17 X[3533], 8 X[1216] + 13 X[15028], 4 X[2979] + 3 X[3060], X[2979] - 8 X[3819], 5 X[2979] - 12 X[3917], 5 X[2979] + 9 X[5640], X[2979] - 36 X[5650], 11 X[2979] + 24 X[5943], 5 X[2979] + 16 X[6688], 2 X[2979] - 9 X[7998], 23 X[2979] + 96 X[10219], 17 X[2979] + 18 X[11002], 2 X[2979] + 5 X[11451], 31 X[2979] + 144 X[12045], 5 X[2979] + 72 X[15082], 31 X[2979] + 18 X[16981], 25 X[2979] + 24 X[21849], 23 X[2979] + 12 X[21969], X[2979] + 27 X[33879], 11 X[2979] - 18 X[33884], 3 X[3060] + 32 X[3819], 5 X[3060] + 16 X[3917], 5 X[3060] - 12 X[5640], X[3060] + 48 X[5650], 11 X[3060] - 32 X[5943], 15 X[3060] - 64 X[6688], X[3060] + 6 X[7998], 23 X[3060] - 128 X[10219], 17 X[3060] - 24 X[11002], 3 X[3060] - 10 X[11451], 31 X[3060] - 192 X[12045], 5 X[3060] - 96 X[15082], 31 X[3060] - 24 X[16981], 25 X[3060] - 32 X[21849], 23 X[3060] - 16 X[21969], X[3060] - 36 X[33879], 11 X[3060] + 24 X[33884], 5 X[3091] + 2 X[36987], 5 X[3522] + 2 X[32062], 2 X[3523] + X[15056], 3 X[3524] + 4 X[10170], 9 X[3524] - 2 X[14855], 6 X[3524] + X[15305], 22 X[3525] - X[5889], 11 X[3525] - 4 X[5892], 2 X[3526] + X[7999], 4 X[3526] - X[15043], 16 X[3530] + 5 X[15058], 34 X[3533] - 13 X[15028], 5 X[3567] + 16 X[32142], 5 X[3620] + 2 X[40673], 20 X[3763] + X[12220], 25 X[3763] - 4 X[41579], 10 X[3819] - 3 X[3917], 40 X[3819] + 9 X[5640], 2 X[3819] - 9 X[5650], 11 X[3819] + 3 X[5943], 5 X[3819] + 2 X[6688], 16 X[3819] - 9 X[7998], 23 X[3819] + 12 X[10219], 68 X[3819] + 9 X[11002], 16 X[3819] + 5 X[11451], 31 X[3819] + 18 X[12045], 5 X[3819] + 9 X[15082], 124 X[3819] + 9 X[16981], 25 X[3819] + 3 X[21849], 46 X[3819] + 3 X[21969], 8 X[3819] + 27 X[33879], 44 X[3819] - 9 X[33884], 5 X[3843] + 16 X[11592], 4 X[3917] + 3 X[5640], X[3917] - 15 X[5650], 11 X[3917] + 10 X[5943], 3 X[3917] + 4 X[6688], 8 X[3917] - 15 X[7998], 23 X[3917] + 40 X[10219], 34 X[3917] + 15 X[11002], 24 X[3917] + 25 X[11451], 31 X[3917] + 60 X[12045], X[3917] + 6 X[15082], 62 X[3917] + 15 X[16981], 5 X[3917] + 2 X[21849], 23 X[3917] + 5 X[21969], 4 X[3917] + 45 X[33879], 22 X[3917] - 15 X[33884], 6 X[5054] + X[11459], 13 X[5067] + 8 X[5447], 13 X[5067] - 6 X[14845], 13 X[5068] + 8 X[13348], 11 X[5070] - 4 X[13364], 4 X[5447] + 3 X[14845], X[5640] + 20 X[5650], 33 X[5640] - 40 X[5943], 9 X[5640] - 16 X[6688], 2 X[5640] + 5 X[7998], 69 X[5640] - 160 X[10219], 17 X[5640] - 10 X[11002], 18 X[5640] - 25 X[11451], 31 X[5640] - 80 X[12045], X[5640] - 8 X[15082], 31 X[5640] - 10 X[16981], 15 X[5640] - 8 X[21849], 69 X[5640] - 20 X[21969], X[5640] - 15 X[33879], 11 X[5640] + 10 X[33884], 33 X[5650] + 2 X[5943], 45 X[5650] + 4 X[6688], 8 X[5650] - X[7998], 69 X[5650] + 8 X[10219], 34 X[5650] + X[11002], 72 X[5650] + 5 X[11451], 31 X[5650] + 4 X[12045], 5 X[5650] + 2 X[15082], 62 X[5650] + X[16981], 75 X[5650] + 2 X[21849], 69 X[5650] + X[21969], 4 X[5650] + 3 X[33879], 22 X[5650] - X[33884], X[5889] - 8 X[5892], 2 X[5890] + 5 X[11444], 5 X[5890] + 2 X[18436], 8 X[5891] - X[12111], 4 X[5891] + 3 X[20791], 5 X[5891] + 2 X[40647], 15 X[5943] - 22 X[6688], 16 X[5943] + 33 X[7998], 23 X[5943] - 44 X[10219], 68 X[5943] - 33 X[11002], 48 X[5943] - 55 X[11451], 31 X[5943] - 66 X[12045], 5 X[5943] - 33 X[15082], 124 X[5943] - 33 X[16981], 25 X[5943] - 11 X[21849], 46 X[5943] - 11 X[21969], 8 X[5943] - 99 X[33879], 4 X[5943] + 3 X[33884], 4 X[6101] + 17 X[11465], X[6241] - 22 X[15720], 32 X[6688] + 45 X[7998], 23 X[6688] - 30 X[10219], 136 X[6688] - 45 X[11002], 32 X[6688] - 25 X[11451], 31 X[6688] - 45 X[12045], 2 X[6688] - 9 X[15082], 248 X[6688] - 45 X[16981], 10 X[6688] - 3 X[21849], 92 X[6688] - 15 X[21969], 16 X[6688] - 135 X[33879], 88 X[6688] + 45 X[33884], 17 X[7486] + 4 X[15644], 69 X[7998] + 64 X[10219], 17 X[7998] + 4 X[11002], 9 X[7998] + 5 X[11451], 31 X[7998] + 32 X[12045], 5 X[7998] + 16 X[15082], 31 X[7998] + 4 X[16981], 75 X[7998] + 16 X[21849], 69 X[7998] + 8 X[21969], X[7998] + 6 X[33879], 11 X[7998] - 4 X[33884], 2 X[7999] + X[15043], 4 X[8703] + 3 X[16261], 2 X[9730] - 9 X[15709], X[9971] - 8 X[34573], 6 X[10170] + X[14855], 8 X[10170] - X[15305], 272 X[10219] - 69 X[11002], 192 X[10219] - 115 X[11451], 62 X[10219] - 69 X[12045], 20 X[10219] - 69 X[15082], 496 X[10219] - 69 X[16981], 100 X[10219] - 23 X[21849], 8 X[10219] - X[21969], 32 X[10219] - 207 X[33879], 176 X[10219] + 69 X[33884], 26 X[10303] - 5 X[10574], 13 X[10303] + 8 X[11793], 5 X[10574] + 16 X[11793], 36 X[11002] - 85 X[11451], 31 X[11002] - 136 X[12045], 5 X[11002] - 68 X[15082], 31 X[11002] - 17 X[16981], 75 X[11002] - 68 X[21849], 69 X[11002] - 34 X[21969], 2 X[11002] - 51 X[33879], 11 X[11002] + 17 X[33884], X[11188] - 8 X[20582], 5 X[11412] + 16 X[16881], 15 X[11439] - 8 X[11455], 85 X[11439] - 64 X[32137], 25 X[11444] - 4 X[18436], 155 X[11451] - 288 X[12045], 25 X[11451] - 144 X[15082], 155 X[11451] - 36 X[16981], 125 X[11451] - 48 X[21849], 115 X[11451] - 24 X[21969], 5 X[11451] - 54 X[33879], 55 X[11451] + 36 X[33884], 17 X[11455] - 24 X[32137], 6 X[11539] + X[23039], 10 X[12045] - 31 X[15082], 8 X[12045] - X[16981], 150 X[12045] - 31 X[21849], 276 X[12045] - 31 X[21969], 16 X[12045] - 93 X[33879], 88 X[12045] + 31 X[33884], X[12111] + 6 X[20791], 5 X[12111] + 16 X[40647], 5 X[12220] + 16 X[41579], X[12279] - 22 X[15717], X[12290] + 20 X[15712], X[13340] + 6 X[15699], 4 X[13363] - 11 X[15723], 2 X[14449] - 23 X[41992], 4 X[14855] + 3 X[15305], 11 X[15024] - 32 X[16239], 2 X[15030] + 5 X[15692], 3 X[15045] + 4 X[15067], 3 X[15045] - 10 X[15694], 2 X[15060] + 5 X[15693], 2 X[15067] + 5 X[15694], 3 X[15072] + 4 X[18435], 124 X[15082] - 5 X[16981], 15 X[15082] - X[21849], 138 X[15082] - 5 X[21969], 8 X[15082] - 15 X[33879], 44 X[15082] + 5 X[33884], X[15100] + 20 X[38794], X[15531] + 6 X[21356], 10 X[15713] - 3 X[40280], 11 X[15721] - 4 X[16836], 2 X[16194] + 5 X[19708], X[16658] + 6 X[43934], 75 X[16981] - 124 X[21849], 69 X[16981] - 62 X[21969], 2 X[16981] - 93 X[33879], 11 X[16981] + 31 X[33884], 15 X[20791] - 8 X[40647], 46 X[21849] - 25 X[21969], 8 X[21849] - 225 X[33879], 44 X[21849] + 75 X[33884], 4 X[21969] - 207 X[33879], 22 X[21969] + 69 X[33884], 20 X[31274] + X[39836], 33 X[33879] + 2 X[33884]
See Francisco Javier García Capitán and Peter Moses, euclid 2027.
X(44299) lies on these lines: {2, 51}, {3, 11439}, {9, 26910}, {25, 41462}, {54, 13154}, {57, 26911}, {110, 7484}, {140, 5890}, {141, 26913}, {154, 5888}, {394, 5646}, {549, 15072}, {568, 10124}, {573, 16057}, {631, 5891}, {632, 11412}, {1154, 3526}, {1180, 21001}, {1194, 8617}, {1216, 3533}, {1368, 7703}, {1401, 9330}, {1613, 15302}, {1994, 22112}, {2393, 3619}, {3091, 36987}, {3522, 32062}, {3523, 6000}, {3524, 10170}, {3525, 5889}, {3530, 15058}, {3567, 32142}, {3620, 40673}, {3688, 9335}, {3763, 12220}, {3784, 35595}, {3843, 11592}, {5012, 10541}, {5020, 21766}, {5054, 11459}, {5067, 5447}, {5068, 13348}, {5070, 13364}, {5092, 44108}, {5644, 15019}, {5651, 15246}, {5663, 15701}, {6030, 35259}, {6101, 11465}, {6241, 15720}, {6617, 39243}, {6636, 10546}, {7486, 15644}, {7495, 41715}, {7496, 9306}, {7509, 11449}, {8703, 16261}, {9730, 15709}, {9971, 34573}, {10303, 10574}, {10601, 23061}, {11004, 34566}, {11064, 33523}, {11188, 20582}, {11202, 37126}, {11205, 36650}, {11402, 15066}, {11422, 43650}, {11539, 23039}, {12279, 15717}, {12290, 15712}, {13340, 15699}, {13363, 15723}, {13391, 15703}, {13595, 16187}, {13754, 15702}, {14449, 41992}, {14915, 15698}, {15024, 16239}, {15030, 15692}, {15045, 15067}, {15060, 15693}, {15100, 38794}, {15531, 21356}, {15713, 40280}, {15721, 16836}, {15801, 15805}, {16194, 19708}, {16658, 43934}, {17534, 37482}, {17582, 41723}, {18950, 41724}, {20859, 39576}, {23293, 30739}, {24206, 31101}, {31255, 40920}, {31274, 39836}, {33540, 35502}
X(44299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2979, 11451}, {2, 3819, 2979}, {2, 3917, 5640}, {2, 7998, 3060}, {2, 33884, 5943}, {631, 5891, 20791}, {1216, 3533, 15028}, {2979, 3819, 7998}, {2979, 11451, 3060}, {3524, 10170, 15305}, {3526, 7999, 15043}, {3819, 6688, 3917}, {3819, 15082, 6688}, {3917, 15082, 2}, {5640, 6688, 11451}, {5640, 33879, 15082}, {5650, 33879, 7998}, {5651, 15246, 26881}, {5891, 20791, 12111}, {7998, 11451, 2979}, {10303, 11793, 10574}, {15067, 15694, 15045}, {17811, 40916, 5012}
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