Τετάρτη 25 Μαρτίου 2026

z

X(71995) = X(2)X(187)∩X(3)X(3734)

Barycentrics    2*a^4 - 3*a^2*b^2 - 3*a^2*c^2 - 2*b^2*c^2 : :
X(71995) = 3 X[2] + X[14907], 3 X[183] - X[17131], 3 X[183] + X[31859], 3 X[574] + X[17131], 3 X[574] - X[31859], 3 X[11168] - X[64093], 5 X[631] - X[9744], X[11185] + 3 X[33008], 3 X[44543] - X[62203]

See Stanley Rabinowitz, Antreas Hatzipolakis and Peter Moses, euclid 9344.

X(71995) lies on these lines: {2, 187}, {3, 3734}, {5, 7830}, {6, 15482}, {15, 69166}, {16, 69159}, {30, 58446}, {32, 6683}, {35, 69256}, {36, 69136}, {39, 385}, {76, 33004}, {83, 35007}, {98, 15483}, {99, 8589}, {115, 8356}, {140, 626}, {141, 542}, {183, 538}, {193, 63952}, {194, 31652}, {230, 4045}, {302, 14905}, {303, 14904}, {315, 31455}, {325, 7810}, {384, 15513}, {474, 36812}, {543, 11168}, {575, 40108}, {599, 7622}, {623, 44223}, {624, 52650}, {631, 3788}, {754, 3815}, {993, 27076}, {1003, 8588}, {1500, 71449}, {1506, 7750}, {1656, 7825}, {1975, 15515}, {2482, 5939}, {2548, 32978}, {2549, 32457}, {2794, 37451}, {2896, 7769}, {3053, 7808}, {3054, 6722}, {3096, 7874}, {3111, 5108}, {3329, 5008}, {3523, 7795}, {3524, 69206}, {3526, 7784}, {3530, 7789}, {3589, 41413}, {3619, 33216}, {3763, 11288}, {3767, 32990}, {3785, 7759}, {3793, 9300}, {3819, 35060}, {3917, 14962}, {4048, 55674}, {5007, 7786}, {5013, 7751}, {5023, 69172}, {5024, 7798}, {5041, 6179}, {5052, 60702}, {5054, 7778}, {5077, 7617}, {5103, 38230}, {5116, 14994}, {5149, 34473}, {5171, 67859}, {5188, 37334}, {5206, 7770}, {5210, 11286}, {5237, 69138}, {5238, 69146}, {5309, 17008}, {5355, 22329}, {5432, 69174}, {5433, 69260}, {5461, 15597}, {5661, 40879}, {6292, 7807}, {6308, 51827}, {6644, 14767}, {6655, 39565}, {6656, 7749}, {6680, 8362}, {6781, 8370}, {7496, 10130}, {7618, 32817}, {7619, 22110}, {7689, 59556}, {7739, 37667}, {7746, 7791}, {7747, 32992}, {7748, 32832}, {7752, 7873}, {7754, 53096}, {7756, 59635}, {7762, 9698}, {7763, 7854}, {7764, 7767}, {7768, 69197}, {7774, 63939}, {7775, 31489}, {7777, 7811}, {7781, 15815}, {7782, 31276}, {7790, 17004}, {7792, 66417}, {7794, 69418}, {7799, 63044}, {7801, 16990}, {7802, 16921}, {7803, 33258}, {7809, 17005}, {7813, 37671}, {7814, 7929}, {7818, 69413}, {7820, 35297}, {7822, 16925}, {7827, 63047}, {7828, 33021}, {7832, 33259}, {7833, 47617}, {7834, 16043}, {7835, 16986}, {7838, 31406}, {7840, 55801}, {7844, 11287}, {7846, 39784}, {7850, 63021}, {7852, 7857}, {7855, 31457}, {7866, 44535}, {7867, 33233}, {7869, 15720}, {7872, 13881}, {7879, 7888}, {7883, 7925}, {7887, 7935}, {7890, 63929}, {7896, 69158}, {7899, 7928}, {7910, 32966}, {7911, 32967}, {7912, 7936}, {7914, 32954}, {7924, 14061}, {7926, 9939}, {7931, 31168}, {7938, 7940}, {7944, 33245}, {7947, 32027}, {8150, 34870}, {8289, 41134}, {8354, 53419}, {8358, 43291}, {8360, 44381}, {8368, 34573}, {8556, 15301}, {8722, 13860}, {8891, 15246}, {9301, 44422}, {9734, 64653}, {9828, 53736}, {10104, 13334}, {10168, 44380}, {10182, 59706}, {11007, 40544}, {11008, 63949}, {11163, 63942}, {11184, 66455}, {11185, 33008}, {11187, 30747}, {12040, 22165}, {12055, 41622}, {12100, 32459}, {13196, 55695}, {13349, 22687}, {13350, 22689}, {13357, 39603}, {13468, 15048}, {14023, 31400}, {14041, 39601}, {14096, 21444}, {14148, 15598}, {14650, 34227}, {14711, 15602}, {14810, 24256}, {14869, 49112}, {15031, 33256}, {15491, 18907}, {15589, 34511}, {15702, 37690}, {15712, 59545}, {16509, 36523}, {16589, 17684}, {18424, 33017}, {18546, 44526}, {18840, 60323}, {18860, 22712}, {19694, 31268}, {24206, 37459}, {26244, 48860}, {30542, 44558}, {31450, 63934}, {31467, 63932}, {32479, 35955}, {32815, 34504}, {32838, 33023}, {32867, 32982}, {32883, 32980}, {32960, 69209}, {32983, 43618}, {32986, 43620}, {33003, 69430}, {33224, 63121}, {33226, 69385}, {33234, 69141}, {33260, 70210}, {33272, 69407}, {33771, 71593}, {36521, 59780}, {37242, 67872}, {37450, 38737}, {37686, 70524}, {41750, 63018}, {43238, 69181}, {43239, 69187}, {43619, 63957}, {44543, 62203}, {47044, 47047}, {50571, 51186}, {50774, 63633}, {52262, 71185}, {52718, 63533}, {52793, 69097}, {53033, 61820}, {53142, 69453}, {55732, 61814}, {59197, 65767}, {59530, 64027}, {63548, 63924}, {67215, 67551}, {68079, 71187}

X(71995) = midpoint of X(i) and X(j) for these {i,j}: {183, 574}, {5475, 14907}, {8722, 13860}, {17131, 31859}
X(71995) = complement of X(5475)
X(71995) = complement of the isogonal conjugate of X(67310)
X(71995) = X(67310)-complementary conjugate of X(10)
X(71995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 187, 7804}, {2, 316, 7603}, {2, 7761, 625}, {2, 7771, 187}, {2, 7831, 7853}, {2, 7934, 31275}, {2, 14907, 5475}, {2, 31173, 66511}, {2, 55164, 31173}, {2, 64018, 31415}, {3, 3734, 32456}, {3, 3934, 7816}, {3, 7815, 3934}, {3, 15271, 3734}, {3, 69139, 69171}, {5, 7830, 7842}, {6, 15482, 44562}, {32, 11285, 6683}, {39, 1078, 7780}, {39, 7780, 7805}, {76, 33004, 37512}, {99, 33273, 8589}, {141, 549, 620}, {141, 620, 7880}, {183, 31859, 17131}, {187, 7771, 46893}, {230, 4045, 7817}, {230, 8359, 4045}, {315, 33001, 31455}, {325, 7810, 7848}, {384, 43459, 15513}, {549, 12042, 5092}, {574, 17131, 31859}, {625, 40344, 7761}, {631, 7800, 3788}, {1078, 7824, 39}, {1506, 7750, 7843}, {2896, 7769, 7821}, {3054, 33184, 6722}, {3096, 7907, 7874}, {3526, 7784, 7862}, {3734, 7815, 15271}, {3734, 15271, 3934}, {3734, 32456, 7816}, {3785, 31401, 7759}, {3788, 7800, 7849}, {3934, 32456, 3734}, {4045, 34506, 230}, {5013, 7751, 32450}, {5024, 8667, 7798}, {6292, 7807, 7915}, {6656, 7749, 7886}, {7496, 10130, 30749}, {7746, 7791, 7861}, {7752, 7904, 7873}, {7756, 59635, 63922}, {7763, 7854, 7895}, {7764, 7767, 7882}, {7777, 7811, 7845}, {7786, 7793, 5007}, {7802, 16921, 39590}, {7804, 46893, 187}, {7853, 15810, 7831}, {7857, 7876, 7852}, {7904, 33015, 7752}, {7924, 17006, 14061}, {7928, 16923, 7899}, {8356, 37688, 115}, {8359, 34506, 7817}, {8556, 53095, 69380}, {8589, 9466, 99}, {11287, 37637, 7844}, {15513, 31239, 384}, {15815, 69381, 7781}, {16043, 69207, 7834}, {16986, 33274, 7835}, {16990, 69450, 7801}, {17004, 66414, 7790}, {31276, 33022, 7782}, {31406, 63928, 7838}, {31415, 64018, 63956}, {32027, 62362, 7947}, {32832, 32965, 7748}, {32990, 69423, 3767}, {33017, 53127, 18424}, {33215, 34229, 2549}, {33234, 69412, 69141}, {43619, 69382, 63957}, {47088, 47089, 5026}


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X(71995) = X(2)X(187)∩X(3)X(3734) Barycentrics    2*a^4 - 3*a^2*b^2 - 3*a^2*c^2 - 2*b^2*c^2 : : X(71995) = 3 X[2] + X[14907], 3 X[183]...