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Results (34 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
10.0.794...688.1 $x^{10} - x^{9} + 17 x^{8} - 56 x^{7} - 139 x^{6} + 1115 x^{5} + 9021 x^{4} + 42044 x^{3} + 155917 x^{2} + 357299 x + 687241$ $-\,2^{12}\cdot 3^{5}\cdot 41^{8}$ $D_{10}$ (as 10T3) $[5]$ $253962.69413235257$
10.2.635...504.1 $x^{10} + 28 x^{8} - 82 x^{7} - 408 x^{6} - 3280 x^{5} - 13117 x^{4} - 11480 x^{3} - 7798 x^{2} - 2624 x - 5972$ $2^{15}\cdot 3^{5}\cdot 41^{8}$ $D_{10}$ (as 10T3) $[5]$ $582192.1229160837$
10.0.188...611.3 $x^{10} - x^{9} + x^{8} + 703 x^{7} - 2749 x^{6} + 5521 x^{5} + 108307 x^{4} - 1082247 x^{3} + 3899732 x^{2} - 8172924 x + 9240419$ $-\,11^{9}\cdot 41^{8}$ $C_{10}$ (as 10T1) $[605]$ $5741.1404574$
10.0.245...279.4 $x^{10} - 4 x^{9} + 40 x^{8} + 94 x^{7} + 8 x^{6} + 3040 x^{5} + 7009 x^{4} + 2840 x^{3} + 139835 x^{2} + 266270 x + 134563$ $-\,41^{8}\cdot 79^{5}$ $A_5\times C_2$ (as 10T11) $[5, 15]$ $4019246.521670347$
10.0.485...000.1 $x^{10} - 328 x^{5} + 107584$ $-\,2^{8}\cdot 3^{5}\cdot 5^{10}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[10]$ $77399001.06722851$
10.0.118...875.1 $x^{10} + 205 x^{8} + 33620 x^{6} - 21853 x^{5} + 1723025 x^{4} - 8959730 x^{3} + 70644025 x^{2} - 183674465 x + 477553609$ $-\,3^{5}\cdot 5^{14}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5]$ $282379319.24883604$
10.0.588...375.1 $x^{10} - 3 x^{9} - 288 x^{8} - 1864 x^{7} + 23544 x^{6} + 455058 x^{5} + 3695288 x^{4} + 18696229 x^{3} + 64828890 x^{2} + 140242725 x + 197510611$ $-\,5^{5}\cdot 11^{9}\cdot 41^{8}$ $C_{10}$ (as 10T1) $[41, 820]$ $5741.140457401364$
10.0.294...875.1 $x^{10} - x^{9} + 375 x^{8} - 1310 x^{7} + 40085 x^{6} - 207703 x^{5} + 1399773 x^{4} - 4540790 x^{3} + 10921175 x^{2} - 13775785 x + 11330265$ $-\,5^{6}\cdot 11^{9}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5, 5]$ $211938177.9326882$
10.0.296...875.1 $x^{10} + 205 x^{8} + 36285 x^{6} - 767889 x^{5} + 5715400 x^{4} - 21180600 x^{3} + 18877630 x^{2} + 65659860 x + 43616907$ $-\,3^{5}\cdot 5^{16}\cdot 41^{8}$ $A_5\times C_2$ (as 10T11) $[5, 15]$ $102270212.80456363$
10.0.819...375.1 $x^{10} - 5 x^{9} - 390 x^{8} + 1590 x^{7} + 54635 x^{6} - 125785 x^{5} - 3268105 x^{4} - 3013290 x^{3} + 80304400 x^{2} + 338675295 x + 423223598$ $-\,5^{14}\cdot 7^{5}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5]$ $1373665405.964629$
10.0.649...875.1 $x^{10} - 2 x^{9} - 178 x^{8} - 940 x^{7} + 31683 x^{6} + 61838 x^{5} - 281442 x^{4} + 88040 x^{3} + 3678337 x^{2} + 2731018 x + 1833316$ $-\,3^{5}\cdot 5^{6}\cdot 11^{8}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5, 5]$ $1549518157.3482177$
10.0.784...875.1 $x^{10} - 5 x^{9} - 385 x^{8} + 1570 x^{7} + 53895 x^{6} - 123495 x^{5} - 3228810 x^{4} - 3532780 x^{3} + 81224545 x^{2} + 365987120 x + 496479329$ $-\,5^{14}\cdot 11^{5}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5]$ $3267820388.0036817$
10.2.121...000.1 $x^{10} - 425 x^{8} + 61385 x^{6} - 43706 x^{5} - 3572395 x^{4} + 7648550 x^{3} + 71000515 x^{2} - 288678130 x + 295080406$ $2^{10}\cdot 3^{5}\cdot 5^{14}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5]$ $4363256615.089077$
10.2.665...000.1 $x^{10} - 4 x^{9} + 353 x^{8} - 104 x^{7} + 33864 x^{6} + 107536 x^{5} + 577512 x^{4} + 1013344 x^{3} + 4995856 x^{2} + 7761536 x - 15005552$ $2^{10}\cdot 3^{5}\cdot 5^{6}\cdot 11^{8}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5, 5, 5]$ $6327756421.905004$
10.0.114...875.1 $x^{10} + 1109460 x^{6} - 3250357 x^{5} - 3350014470 x^{3} + 136766832400 x^{2} + 1202047025740 x + 4158510460687$ $-\,5^{14}\cdot 11^{9}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5, 5, 5]$ $18171005762.444405$
10.0.253...875.1 $x^{10} - 2255 x^{8} + 4068020 x^{6} - 203401 x^{5} - 2293346275 x^{4} + 917338510 x^{3} + 1034299170025 x^{2} - 206859834005 x + 41371966801$ $-\,3^{5}\cdot 5^{14}\cdot 11^{8}\cdot 41^{8}$ $F_{5}\times C_2$ (as 10T5) $[5, 5, 5]$ $152641874399.10318$
10.0.328...875.1 $x^{10} - x^{9} + 1657 x^{8} - 88452 x^{7} + 3254031 x^{6} - 73793268 x^{5} + 1258854858 x^{4} - 15229904958 x^{3} + 138934643229 x^{2} - 816359497758 x + 3060533315844$ $-\,3^{5}\cdot 5^{6}\cdot 41^{8}\cdot 101^{8}$ $F_{5}\times C_2$ (as 10T5) $[5, 5]$ $9311135404024.12$
10.0.322...875.1 $x^{10} - x^{9} - 3919 x^{8} + 468000 x^{7} + 7306840 x^{6} - 1012165680 x^{5} + 24905759920 x^{4} - 1039715164800 x^{3} + 36940306467200 x^{2} - 804654756448000 x + 10578056676102400$ $-\,3^{5}\cdot 5^{6}\cdot 41^{8}\cdot 239^{8}$ $F_{5}\times C_2$ (as 10T5) $[5, 5]$ $303066841016740.94$
12.4.311...801.1 $x^{12} - 4 x^{11} + 2 x^{10} + 13 x^{9} - 55 x^{8} + 5 x^{7} - 21 x^{6} - 8 x^{5} - 285 x^{4} + 557 x^{3} - 490 x^{2} + 224 x - 40$ $41^{8}\cdot 79^{4}$ $C_2\times A_5$ (as 12T76) trivial $646762.8045308752$
12.4.986...625.1 $x^{12} - x^{11} + 22 x^{10} + 65 x^{9} - 755 x^{8} + 3669 x^{7} - 13894 x^{6} + 8118 x^{5} + 65920 x^{4} - 295700 x^{3} - 688589 x^{2} - 854921 x - 753743$ $3^{4}\cdot 5^{16}\cdot 41^{8}$ $C_2\times A_5$ (as 12T76) trivial $273555130.41668713$
20.0.404...016.3 $x^{20} - 18 x^{18} + 55 x^{16} + 14 x^{14} + 14381 x^{12} - 190396 x^{10} + 1133340 x^{8} - 7116528 x^{6} + 79490576 x^{4} - 730931200 x^{2} + 2621440000$ $2^{30}\cdot 3^{10}\cdot 41^{16}$ $D_{10}$ (as 20T4) $[5]$ $739275400192$
20.4.175...125.2 $x^{20} - 5 x^{19} - 10 x^{18} + 90 x^{17} - 30 x^{16} - 44327 x^{15} + 185720 x^{14} - 931035 x^{13} + 4441940 x^{12} - 11163630 x^{11} + 726879449 x^{10} - 2255686960 x^{9} + 21188171680 x^{8} - 50195349995 x^{7} + 188317019190 x^{6} - 5311713092173 x^{5} + 9078536800910 x^{4} - 109418242556830 x^{3} + 37301023424470 x^{2} - 176293968831715 x + 13427265857210251$ $3^{10}\cdot 5^{31}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) $[5]$ $464655797254258800$
20.20.108...125.1 $x^{20} - x^{19} - 724 x^{18} + 1933 x^{17} + 207069 x^{16} - 879414 x^{15} - 29244939 x^{14} + 168000394 x^{13} + 2068450902 x^{12} - 15163663108 x^{11} - 65471435699 x^{10} + 640279637052 x^{9} + 723107842172 x^{8} - 12962056979224 x^{7} + 1904187630105 x^{6} + 126523888290302 x^{5} - 49209916894584 x^{4} - 625770152130483 x^{3} + 20489361496947 x^{2} + 1354721938371869 x + 874798166506991$ $5^{15}\cdot 11^{18}\cdot 41^{16}$ $C_{20}$ (as 20T1) $[5, 55]$ $3313588880654819000$
20.4.108...125.3 $x^{20} - 8 x^{19} - 156 x^{18} - 952 x^{17} + 17527 x^{16} + 241902 x^{15} - 1136451 x^{14} - 21143487 x^{13} + 32888707 x^{12} + 309949732 x^{11} - 8399093196 x^{10} + 50338298318 x^{9} + 193793523407 x^{8} - 3449484980348 x^{7} - 29815059450616 x^{6} + 19997778190588 x^{5} - 750024162066003 x^{4} + 2346903326902332 x^{3} + 8078639162151899 x^{2} + 16769387472122923 x + 53854635816438281$ $5^{15}\cdot 11^{18}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) $[5, 5, 5]$ $1189076316751181600$
20.4.838...125.2 $x^{20} - 5 x^{19} - 35 x^{18} + 215 x^{17} + 420 x^{16} + 39885 x^{15} - 185975 x^{14} + 1641450 x^{13} - 9551200 x^{12} + 14329275 x^{11} + 696150660 x^{10} - 2107342900 x^{9} + 41741808575 x^{8} - 105758201050 x^{7} + 911902235600 x^{6} + 3715280644050 x^{5} - 5344988560625 x^{4} + 221169857291125 x^{3} - 60583973026250 x^{2} + 691307088931500 x + 13445341298628775$ $5^{31}\cdot 7^{10}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) $[5]$ $31758563963704467000$
20.20.527...125.1 $x^{20} - x^{19} - 743 x^{18} - 4445 x^{17} + 199349 x^{16} + 2649082 x^{15} - 11934227 x^{14} - 462688016 x^{13} - 2960203530 x^{12} + 10967480614 x^{11} + 298540044700 x^{10} + 2300021254716 x^{9} + 10317097607687 x^{8} + 30084574861329 x^{7} + 58187584685882 x^{6} + 73096633116390 x^{5} + 56241787999723 x^{4} + 23628273816896 x^{3} + 4243278452968 x^{2} + 37501809775 x - 36559534769$ $3^{10}\cdot 5^{15}\cdot 11^{16}\cdot 41^{16}$ $C_{20}$ (as 20T1) $[5, 55]$ $69785404682060825000$
20.4.527...125.4 $x^{20} - 3 x^{19} + 704 x^{18} + 118 x^{17} + 191036 x^{16} + 621355 x^{15} + 25952480 x^{14} + 152340840 x^{13} + 1971122200 x^{12} + 13163384025 x^{11} + 86651330850 x^{10} + 394824371800 x^{9} + 1632921305900 x^{8} + 5476552554375 x^{7} + 15851601582000 x^{6} + 37483461188250 x^{5} + 61786944137500 x^{4} + 64360969638125 x^{3} - 59977480092500 x^{2} - 235060150812500 x - 97632094274375$ $3^{10}\cdot 5^{15}\cdot 11^{16}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) not computed
20.4.770...125.2 $x^{20} - 5 x^{19} - 60 x^{18} + 340 x^{17} + 1420 x^{16} + 33985 x^{15} - 200850 x^{14} + 2429525 x^{13} - 14548850 x^{12} + 4035250 x^{11} + 732177235 x^{10} - 1773551650 x^{9} + 62360222700 x^{8} - 165461971925 x^{7} + 2199112430850 x^{6} + 1732196730925 x^{5} + 3755155905000 x^{4} + 324189057741500 x^{3} - 66040638710750 x^{2} + 1533110625113875 x + 13502138530056025$ $5^{31}\cdot 11^{10}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) not computed
20.0.183...000.1 $x^{20} + 75 x^{18} + 2475 x^{16} - 43706 x^{15} + 47250 x^{14} + 1260750 x^{13} + 577125 x^{12} + 52195050 x^{11} + 713974136 x^{10} + 907740000 x^{9} - 58891146225 x^{8} + 8748344250 x^{7} + 2605588611300 x^{6} - 5026643409406 x^{5} - 13485012397875 x^{4} + 408977847905100 x^{3} + 34962741959625 x^{2} - 1928411968953150 x + 13447465084398901$ $2^{20}\cdot 3^{10}\cdot 5^{31}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) not computed
20.0.553...000.1 $x^{20} - 8 x^{19} + 827 x^{18} - 3788 x^{17} + 250847 x^{16} - 402576 x^{15} + 36437906 x^{14} + 34594296 x^{13} + 2865002261 x^{12} + 8030807016 x^{11} + 130500535301 x^{10} + 459158455436 x^{9} + 3271773532861 x^{8} + 10370138231536 x^{7} + 39395124083066 x^{6} + 89066757345784 x^{5} + 183584573751647 x^{4} + 241818819298392 x^{3} + 236849218863987 x^{2} + 133978133142772 x + 29301308648281$ $2^{20}\cdot 3^{10}\cdot 5^{15}\cdot 11^{16}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) not computed
20.4.165...125.1 $x^{20} - 5279406 x^{15} - 172313849975839 x^{10} - 2105583058003554756 x^{5} + 2161732704559354333451$ $5^{31}\cdot 11^{18}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) not computed
20.4.805...125.1 $x^{20} - 5 x^{19} - 10 x^{18} + 90 x^{17} - 30 x^{16} - 407423 x^{15} + 49834055 x^{14} - 393579015 x^{13} + 1965866360 x^{12} - 4770772245 x^{11} - 37272899052151 x^{10} + 83367038323940 x^{9} - 2582431876535120 x^{8} + 5782947973302805 x^{7} - 28856314636775310 x^{6} + 7634573862225014948 x^{5} - 910904292040050710935 x^{4} - 1631889492627330563620 x^{3} - 9032642287154091001520 x^{2} - 2428923132613769730160 x + 348145615950127322894508976$ $3^{10}\cdot 5^{31}\cdot 11^{16}\cdot 41^{16}$ $C_2\times F_5$ (as 20T9) not computed
20.4.134...125.1 $x^{20} - x^{19} - 6647 x^{18} - 170249 x^{17} + 14915602 x^{16} + 858788163 x^{15} + 1550080534 x^{14} - 1187423231617 x^{13} - 42799005665569 x^{12} - 335316962446898 x^{11} + 23067640190101639 x^{10} + 1052843965918740698 x^{9} + 24709431598983134171 x^{8} + 393114849569200158787 x^{7} + 4553829768991818363034 x^{6} + 39237341054811473407482 x^{5} + 250658574766892932525627 x^{4} + 1158949780479443771952134 x^{3} + 3680341867252021169078608 x^{2} + 7201661139240484003038976 x + 6560907147162683525023696$ $3^{10}\cdot 5^{15}\cdot 41^{16}\cdot 101^{16}$ $C_2\times F_5$ (as 20T9) not computed
20.4.130...125.1 $x^{20} - x^{19} + 15657 x^{18} + 920351 x^{17} + 122070168 x^{16} + 11286895689 x^{15} + 922295199477 x^{14} + 68784360932761 x^{13} + 4822333287362703 x^{12} + 302118889484782554 x^{11} + 16876049312187036596 x^{10} + 855869581170661539632 x^{9} + 39006937259889830571976 x^{8} + 1539478120182722547062578 x^{7} + 50451289343820771218160854 x^{6} + 1327323447462215983924725904 x^{5} + 27202303053881763557321670529 x^{4} + 418656891883642941476130818247 x^{3} + 4567258204753622895789583214351 x^{2} + 31535555131810266766082849478093 x + 103138856018920371823015008654121$ $3^{10}\cdot 5^{15}\cdot 41^{16}\cdot 239^{16}$ $C_2\times F_5$ (as 20T9) not computed
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