{"count": 3, "status":"OK", "data":[{"pols": "[X^4, -144-1536*X-6288*X^2-9504*X^3+432*X^4, 92160+497664*X-1492992*X^2-22394880*X^3-8957952*X^4, -398131200-3439853568*X-10749542400*X^2-15479341056*X^3-14189395968*X^4, -55037657088*(3*X+1)^2*(3*X+2)^2]", "text": "Sporadic Operator.", "degz": 4, "h3": "4", "sol": "1 144 147600 239904000 479672701200 1078954420287744 2618634987667835136 6702283021504364236800 17840666902138413842480400 48944005664385888179529120000", "n_discr_factors": "3", "c3": "-18", "operator": "4 4 0 0 0 0 1 -144 -1536 -6288 -9504 432 92160 497664 -1492992 -22394880 -8957952 -398131200 -3439853568 -10749542400 -15479341056 -14189395968 -220150628352 -1981355655168 -6439405879296 -8916100448256 -4458050224128", "new_number": "4.47", "id": 145, "operator_tex": "\\theta^4+2^{4} 3 x\\left(9\\theta^4-198\\theta^3-131\\theta^2-32\\theta-3\\right)-2^{11} 3^{2} x^{2}\\left(486\\theta^4+1215\\theta^3+81\\theta^2-27\\theta-5\\right)-2^{16} 3^{5} x^{3}\\left(891\\theta^4+972\\theta^3+675\\theta^2+216\\theta+25\\right)-2^{23} 3^{8} x^{4}(3\\theta+1)^2(3\\theta+2)^2", "superseek": "1584 171534960", "discriminant": "4 1 432 -8957952 -14189395968 -4458050224128", "aesz": "239", "n_sing_complex": "0", "inst_int": "", "c2h": "28", "hash": "8e610c3437d7f38e552038bc55399495", "dim_h": "3", "inst": " 1584 -17874 171534960 30012731550 105934107802896 63775249469817750 127749832497630077616 131860871041114114038054 224001851211067044692907648 298697681537718689647638089370", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(432z+1)(3456z-1)(1+1728z)^2", "discr_factors": "-4458050224128, z+1/432, z-1/3456, (1/1728+z)^2", "dm_basis": null, "q": "0 1 -960 456480 -333224960 150643621680 -220108476321792 37434112216317440 -259405759761365729280 -112198587502907767173480", "yuk": "1 1584 -141408 4631445504 1920814677792 13241763475363584 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-458535168*X^4-302330880*X^3-186437376*X^2-67184640*X-8709120, 53747712*(3*X+1)^2*(3*X+2)^2]", "text": "Sporadic Operator.", "degz": 4, "h3": null, "sol": "1 72 41400 37396800 41397463800 51465849507072 68974101299847744 97431256231311974400 143088412046096191217400 216526904351285764733640000", "n_discr_factors": "2", "c3": null, "operator": "4 4 0 0 0 0 25 -1800 -17850 -63615 -91530 -52245 -213120 -1244160 69984 10240992 9051264 -8709120 -67184640 -186437376 -302330880 -458535168 214990848 1934917632 6288482304 8707129344 4353564672", "new_number": "4.68", "id": 168, "operator_tex": "5^{2} \\theta^4-3 5 x\\left(3483\\theta^4+6102\\theta^3+4241\\theta^2+1190\\theta+120\\right)+2^{5} 3^{2} x^{2}\\left(31428\\theta^4+35559\\theta^3+243\\theta^2-4320\\theta-740\\right)-2^{8} 3^{5} x^{3}\\left(7371\\theta^4+4860\\theta^3+2997\\theta^2+1080\\theta+140\\right)+2^{13} 3^{8} x^{4}(3\\theta+1)^2(3\\theta+2)^2", "superseek": "2043/5 88982631/5", "discriminant": "4 25 -52245 9051264 -458535168 4353564672", "aesz": "337", "n_sing_complex": "1", "inst_int": "", "c2h": null, "hash": "dc26e94a7c1daba6f627be36c42019b7", "dim_h": null, "inst": " 2043/5 279018/5 88982631/5 8604708876 25774859896713/5 17683308060957072/5 13325172014008420146/5 10754726369310113746644/5 1829462967322461406625346 8108517336265913904915653934/5", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "3", "laurent": null, "discriminant_tex": "(23328z^2-1917z+1)(-5+432z)^2", "discr_factors": "4353564672, (-5/432+z)^2, z^2-71/864*z+1/23328", "dm_basis": null, "q": "0 1 -426 27621 -13241608 -7686485202 -6081843427074 -5184549890041414 -4670074254201955296 -4386070348249547118789", "yuk": "1 2043/5 2234187/5 480506616 2753509074507/5 3221857487091168/5 3819594543571492776/5 4570534000804888112121/5 1101283980217906349471247 1333678503178074365910383850", "gv2": null, "gv0": null, "gv1": null, 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"A-incarnation: X(3,3) in P^5.", "degz": 1, "h3": "9", "sol": "1 36 8100 2822400 1200622500 572679643536 294230074634496 159259227403161600 89595913068008532900 51926300783585192250000", "n_discr_factors": "1", "c3": "-144", "operator": "4 1 0 0 0 0 1 -36 -324 -1053 -1458 -729", "new_number": "1.4", "id": 560, "operator_tex": "\\theta^4-3^{2} x(3\\theta+1)^2(3\\theta+2)^2", "superseek": "117 713814", "discriminant": "1 1 -729", "aesz": "4", "n_sing_complex": "0", "inst_int": null, "c2h": "54", "hash": "1f2a9672b7cdc68eae658b2304b40dbd", "dim_h": "6", "inst": " 117 5868 713814 126605376 27754210287 6962329389948 1917383766758001 565426952047351440 175694524219617543105 56893915767467678536512", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "A_{n}=\\dbinom{2n}{n}^2\\dbinom{3n}{n}^2", "n_sing_rational": "2", "n_sing": "2", "laurent": null, "discriminant_tex": "1-729z", "discr_factors": "-729, -1/729+z", "dm_basis": null, "q": "0 1 -180 8910 -948840 -106787835 -36085459176 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