{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(17*X^2+17*X+6), 1152*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "Hadamard product $C \\ast g$", "degz": 2, "h3": "24", "sol": "1 72 17640 5765760 2156754600 873251451072 372637196515584 165110467068518400 75269439109043922600 35089980080429298024000", "n_discr_factors": "2", "c3": "-344", "operator": "4 2 0 0 0 0 1 -72 -588 -1676 -2176 -1088 120960 811008 1585152 1179648 294912", "new_number": "2.26", "id": 18, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(17\\theta^2+17\\theta+6)+2^{7} 3^{2} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "44 22500", "discriminant": "2 1 -1088 294912", "aesz": "139", "n_sing_complex": "0", "inst_int": "", "c2h": "120", "hash": "f5d9215987323abcff6ed8709927af5d", "dim_h": "14", "inst": " 44 607 22500 1444678 128626784 13469917781 1522820820452 179595469620910 21853624667881360 2736519633179452216", "cleanlist": "True", "n_sing_real": "3", 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{"pols": "[X^4, -4*(2*X+1)^2*(3*X^2+3*X+1), -16*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "A-Incarnation: (1,1) and (2,2) intersection in $P^3 \\times P^3$", "degz": 2, "h3": "40", "sol": "1 4 108 3280 126700 5355504 243791856 11651694912 578075329260 29514351895600", "n_discr_factors": "2", "c3": "-128", "operator": "4 2 0 0 0 0 1 -4 -28 -76 -96 -48 -720 -3456 -5824 -4096 -1024", "new_number": "2.60", "id": 56, "operator_tex": "\\theta^4-2^{2} x(2\\theta+1)^2(3\\theta^2+3\\theta+1)-2^{4} x^{2}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "4 364", "discriminant": "2 1 -48 -1024", "aesz": "18", "n_sing_complex": "0", "inst_int": "", "c2h": "88", "hash": "bb479f8a4185bf4a943dba2d433e13e5", "dim_h": "14", "inst": " 4 39 364 6800 662416/5 3162589 80141644 2204992496 63488383784 9551133342652/5", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(16z+1)(64z-1)", "discr_factors": "-1024, z-1/64, z+1/16", "dm_basis": ["-310145437/500000000*I", "31/3", "1", "1", "-11/3", "-20", "-1", "0", "0", "40", "0", "0", "-40", "0", "0", "0"], "q": "0 1 -12 -90 848 -14079 -313608 -8135374 -247756992 -8049920748", "yuk": "1 4 316 9832 435516 16560404 683129368 27488583896 1128956593468 46283031788368", "gv2": null, "gv0": null, "gv1": null, 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{"pols": "[X^4, -65*X^4-130*X^3-105*X^2-40*X-6, 4*(4*X+3)*(X+1)^2*(4*X+5)]", "text": "A-incarnation: $X(1, 1, 1, 1, 1, 1) \\subset  Grass(3, 6)$", "degz": 2, "h3": "42", "sol": "1 6 126 3948 149310 6300756 285675516 13625781336 674863457598 34412622769140", "n_discr_factors": "2", "c3": "-96", "operator": "4 2 0 0 0 0 1 -6 -40 -105 -130 -65 60 248 380 256 64", "new_number": "2.62", "id": 58, "operator_tex": "\\theta^4-x\\left(65\\theta^4+130\\theta^3+105\\theta^2+40\\theta+6\\right)+2^{2} x^{2}(4\\theta+3)(\\theta+1)^2(4\\theta+5)", "superseek": "5 312", "discriminant": "2 1 -65 64", "aesz": "28", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "06dd455cafc5097e4f671d385984c1a2", "dim_h": "14", "inst": " 5 28 312 4808 91048 1965908 325780668/7 1178954560 31456810796 874502186004", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "(64z-1)(z-1)", "discr_factors": "64, z-1/64, z-1", "dm_basis": ["-96*lambda", "21/2", "1", "1", "-7/2", "-21", "-1", "0", "0", "42", "0", "0", "-42", "0", "0", "0"], "q": "0 1 -16 64 -552 -5632 -165472 -4342772 -123146768 -3627953792", "yuk": "1 5 229 8429 307941 11381005 424644781 15963252737 603625042661 22932015078713", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","42","1","0","0","0","1","1"]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1+96*lambda","0","8*lambda",".5153046e-2","7/2","1","7/24","-8*lambda","0","0","1","0","42","0","7/2","1-96*lambda"],"monodromy_dm":["1","-14","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["16.+8.373926794*I","-5-576*lambda","5/4+144*lambda","-.204864220-.332298682*I","63","-20","21/4","-5/4-144*lambda","252","-84","22","-5-576*lambda","756+1/500000000*I","-252","63","-14.-8.373926794*I"],"monodromy_dm":["-35","-378","-24","-18","12","127","8","6","-252","-2646","-167","-126","156","1638","104","79"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/4","1","1","5/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, 7*X*(-14-73*X-118*X^2+13*X^3), -56448-267792*X-452856*X^2-322704*X^3-81072*X^4, -2325456-9761472*X-13680576*X^2-7741440*X^3-1567296*X^4, -6912*(2*X+1)*(572*X^3+2370*X^2+2896*X+1095), -82944*(2*X+1)*(6*X+5)*(6*X+7)*(2*X+3)]", "text": "This is operator \"5.34\" from ...", "degz": 5, "h3": "42", "sol": "1 0 72 720 37800 907200 36867600 1210809600 47562114600 1773634262400", "n_discr_factors": "4", "c3": "-112", "operator": "4 5 0 0 0 0 49 0 -98 -511 -826 91 -56448 -267792 -452856 -322704 -81072 -2325456 -9761472 -13680576 -7741440 -1567296 -7568640 -35154432 -56415744 -36716544 -7907328 -8709120 -41140224 -68345856 -47775744 -11943936", "new_number": "5.34", "id": 243, "operator_tex": "7^{2} \\theta^4+7 x\\theta(-14-73\\theta-118\\theta^2+13\\theta^3)-2^{3} 3 x^{2}\\left(3378\\theta^4+13446\\theta^3+18869\\theta^2+11158\\theta+2352\\right)-2^{4} 3^{3} x^{3}\\left(3628\\theta^4+17920\\theta^3+31668\\theta^2+22596\\theta+5383\\right)-2^{8} 3^{3} x^{4}(2\\theta+1)(572\\theta^3+2370\\theta^2+2896\\theta+1095)-2^{10} 3^{4} x^{5}(2\\theta+1)(6\\theta+5)(6\\theta+7)(2\\theta+3)", "superseek": "17/7 5095/21", "discriminant": "5 49 91 -81072 -1567296 -7907328 -11943936", "aesz": "217", "n_sing_complex": "0", "inst_int": "", "c2h": "84", "hash": "e8743aeac19deca699ff90aaef6b8ea7", "dim_h": "14", "inst": " 17/7 254/7 5095/21 29600/7 491991/7 4555616/3 232427670/7 5701763664/7 143522855316/7 3818318314434/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "5", "laurent": null, "discriminant_tex": "-(16z+1)(27z+1)(48z-1)(7+24z)^2", "discr_factors": "-11943936, (7/24+z)^2, z+1/27, z+1/16, z-1/48", "dm_basis": null, "q": "0 1 -2 -195 -904 6482 -107274 -6762194 -156595136 -4062227319", "yuk": "1 17/7 2049/7 45872/7 1896449/7 8785556 2296078368/7 79722690827/7 2919304892417/7 104628161571236/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-7/24","im":"0","approx_re":"-0.291666666667","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/27","im":"0","approx_re":"-0.037037037037","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48","im":"0","approx_re":"0.0208333333333","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","5/6","7/6","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(10*X^2+10*X+3), 3344*X^4+16832*X^3+23536*X^2+13408*X+2928, 34560*X^4-207360*X^3-634752*X^2-480384*X-127872, -2092032*X^4-4184064*X^3+5068800*X^2+7160832*X+2405376, 9953280*X^4+99532800*X^3+56070144*X^2-8294400*X-11612160, 277364736*X^4-286654464*X^3-571981824*X^2-286654464*X-35831808, -95551488*(3*X^2+3*X+1)*(10*X^2+10*X+3), 6879707136*(X+1)^4]", "text": "Hadamard product $c \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers. It\ncan be reduced to an operator of degree 4 with a single \nMUM-point defined over $\\Q(\\sqrt{?})$.", "degz": 8, "h3": "48", "sol": "1 12 300 10416 431964 20026512 1002175824 52995470400 2920544068572 166150997604048", "n_discr_factors": "5", "c3": "28", "operator": "4 8 0 0 0 0 1 -12 -76 -196 -240 -120 2928 13408 23536 16832 3344 -127872 -480384 -634752 -207360 34560 2405376 7160832 5068800 -4184064 -2092032 -11612160 -8294400 56070144 99532800 9953280 -35831808 -286654464 -571981824 -286654464 277364736 -286654464 -1815478272 -4682022912 -5733089280 -2866544640 6879707136 27518828544 41278242816 27518828544 6879707136", "new_number": "8.10", "id": 453, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{4} x^{2}\\left(209\\theta^4+1052\\theta^3+1471\\theta^2+838\\theta+183\\right)+2^{7} 3^{2} x^{3}\\left(30\\theta^4-180\\theta^3-551\\theta^2-417\\theta-111\\right)-2^{10} 3^{2} x^{4}\\left(227\\theta^4+454\\theta^3-550\\theta^2-777\\theta-261\\right)+2^{12} 3^{4} x^{5}\\left(30\\theta^4+300\\theta^3+169\\theta^2-25\\theta-35\\right)+2^{14} 3^{4} x^{6}\\left(209\\theta^4-216\\theta^3-431\\theta^2-216\\theta-27\\right)-2^{17} 3^{6} x^{7}(3\\theta^2+3\\theta+1)(10\\theta^2+10\\theta+3)+2^{20} 3^{8} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "12 1828/3", "discriminant": "8 1 -120 3344 34560 -2092032 9953280 277364736 -2866544640 6879707136", "aesz": "123", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "f0d76ab2b6b8808f4faa4ab8ecadff2c", "dim_h": "14", "inst": " 12 -47/2 1828/3 -10813/4 127948 -1853581/6 39969036 280168449/4 50657172196/3 256398596897/2", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "5", "n_sing": "7", "laurent": null, "discriminant_tex": "(36z-1)(8z-1)(72z-1)(4z-1)(-1+288z^2)^2", "discr_factors": "6879707136, z-1/8, z-1/36, (-1/288+z^2)^2, z-1/4, z-1/72", "dm_basis": null, "q": "0 1 -28 572 -11744 233550 -4947920 102001240 -2228888832 46514995429", "yuk": "1 12 -176 16464 -173184 15993512 -66712640 13709379360 35861388288 12309692860092", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/24*2^(1/2)","im":"0","approx_re":"-0.058926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/72","im":"0","approx_re":"0.0138888888889","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/24*2^(1/2)","im":"0","approx_re":"0.058926","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/4","im":"0","approx_re":"0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -4*(3*X^2+3*X+1)*(7*X^2+7*X+2), 1440*X^4+2688*X^3+3744*X^2+2112*X+384, -21504*X^4+129024*X^3+395264*X^2+297984*X+77824, 606208*X^4+1212416*X^3+819200*X^2+212992*X+98304, 5505024*X^4+55050240*X^3+30932992*X^2-4980736*X-6291456, 94371840*X^4+201326592*X^3+283115520*X^2+201326592*X+50331648, 67108864*(3*X^2+3*X+1)*(7*X^2+7*X+2), 4294967296*(X+1)^4]", "text": "Hadamard product $a \\ast d$. This operator has a second MUM-point at infinity with the same instanton numbers.\nIt can be reduced to an operator of degree 4 with a single MUM-point defined over\n$Q(\\sqrt{-1})$.", "degz": 8, "h3": "48", "sol": "1 8 200 6272 233896 9692608 432683264 20387430400 1000461680296 50660529892928", "n_discr_factors": "5", "c3": "12", "operator": "4 8 0 0 0 0 1 -8 -52 -136 -168 -84 384 2112 3744 2688 1440 77824 297984 395264 129024 -21504 98304 212992 819200 1212416 606208 -6291456 -4980736 30932992 55050240 5505024 50331648 201326592 283115520 201326592 94371840 134217728 872415232 2281701376 2818572288 1409286144 4294967296 17179869184 25769803776 17179869184 4294967296", "new_number": "8.3", "id": 485, "operator_tex": "\\theta^4-2^{2} x(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{5} 3 x^{2}\\left(15\\theta^4+28\\theta^3+39\\theta^2+22\\theta+4\\right)-2^{10} x^{3}\\left(21\\theta^4-126\\theta^3-386\\theta^2-291\\theta-76\\right)+2^{14} x^{4}\\left(37\\theta^4+74\\theta^3+50\\theta^2+13\\theta+6\\right)+2^{18} x^{5}\\left(21\\theta^4+210\\theta^3+118\\theta^2-19\\theta-24\\right)+2^{21} 3 x^{6}\\left(15\\theta^4+32\\theta^3+45\\theta^2+32\\theta+8\\right)+2^{26} x^{7}(3\\theta^2+3\\theta+1)(7\\theta^2+7\\theta+2)+2^{32} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "8 -104", "discriminant": "8 1 -84 1440 -21504 606208 5505024 94371840 1409286144 4294967296", "aesz": "105", "n_sing_complex": "2", "inst_int": "", "c2h": "72", "hash": "7b27135451cf2016217211c633b7ab83", "dim_h": "14", "inst": " 8 71/2 -104 4202 50112 1190589/2 19232792 750651197/2 8202541856 213407759180", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "(8z+1)(64z-1)(4z+1)(32z-1)(1+256z^2)^2", "discr_factors": "4294967296, z-1/32, (1/256+z^2)^2, z+1/8, z+1/4, z-1/64", "dm_basis": null, "q": "0 1 -20 150 912 -51715 530216 -531590 -169210560 1317153558", "yuk": "1 8 292 -2800 269220 6264008 128581096 6596847664 192166975652 5979653010224", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"-1/16","approx_re":"0.0","approx_im":"-0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"1/16","approx_re":"0.0","approx_im":"0.0625","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/64","im":"0","approx_re":"0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/32","im":"0","approx_re":"0.03125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}]}