Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
10.0.188...008.1 | $x^{10} - 2 x^{9} + 478 x^{8} - 762 x^{7} + 92942 x^{6} - 111194 x^{5} + 9184335 x^{4} - 7359364 x^{3} + 461126266 x^{2} - 186336424 x + 9409989401$ | $-\,2^{10}\cdot 11^{8}\cdot 97^{5}$ | $C_{10}$ (as 10T1) | $[106084]$ |
10.0.221...888.1 | $x^{10} + 682 x^{8} + 169136 x^{6} + 18351256 x^{4} + 812698480 x^{2} + 10077461152$ | $-\,2^{15}\cdot 11^{9}\cdot 31^{5}$ | $C_{10}$ (as 10T1) | $[2, 57606]$ |
10.0.264...387.1 | $x^{10} - x^{9} + 705 x^{8} - 705 x^{7} + 180929 x^{6} - 180929 x^{5} + 20366017 x^{4} - 20366017 x^{3} + 943112897 x^{2} - 943112897 x + 12754272961$ | $-\,11^{9}\cdot 257^{5}$ | $C_{10}$ (as 10T1) | $[146728]$ |
10.0.293...744.1 | $x^{10} - 2 x^{9} + 523 x^{8} - 834 x^{7} + 111104 x^{6} - 132956 x^{5} + 11978835 x^{4} - 9597214 x^{3} + 655329103 x^{2} - 264585970 x + 14552228339$ | $-\,2^{15}\cdot 11^{8}\cdot 53^{5}$ | $C_{10}$ (as 10T1) | $[148830]$ |
10.0.308...875.1 | $x^{10} - x^{9} + 727 x^{8} - 727 x^{7} + 192391 x^{6} - 192391 x^{5} + 22329583 x^{4} - 22329583 x^{3} + 1065940063 x^{2} - 1065940063 x + 14841598399$ | $-\,5^{5}\cdot 11^{9}\cdot 53^{5}$ | $C_{10}$ (as 10T1) | $[2, 78492]$ |
10.0.318...031.1 | $x^{10} - 3 x^{9} + 534 x^{8} - 1276 x^{7} + 115570 x^{6} - 206320 x^{5} + 12666450 x^{4} - 15024933 x^{3} + 702954614 x^{2} - 415692869 x + 15805781531$ | $-\,11^{8}\cdot 431^{5}$ | $C_{10}$ (as 10T1) | $[107205]$ |
10.0.332...159.1 | $x^{10} - x^{9} + 738 x^{8} - 738 x^{7} + 198254 x^{6} - 198254 x^{5} + 23357005 x^{4} - 23357005 x^{3} + 1131668660 x^{2} - 1131668660 x + 15983044837$ | $-\,11^{9}\cdot 269^{5}$ | $C_{10}$ (as 10T1) | $[134200]$ |
10.0.333...875.1 | $x^{10} - 3 x^{9} + 539 x^{8} - 1288 x^{7} + 117730 x^{6} - 210192 x^{5} + 13020916 x^{4} - 15447017 x^{3} + 729137299 x^{2} - 431232345 x + 16540288711$ | $-\,3^{5}\cdot 5^{5}\cdot 11^{8}\cdot 29^{5}$ | $C_{10}$ (as 10T1) | $[22, 7810]$ |
10.0.337...056.1 | $x^{10} - 2 x^{9} + 538 x^{8} - 858 x^{7} + 117518 x^{6} - 140642 x^{5} + 13022871 x^{4} - 10433236 x^{3} + 731977186 x^{2} - 295457368 x + 16693341281$ | $-\,2^{10}\cdot 11^{8}\cdot 109^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 2, 8130]$ |
10.0.382...167.1 | $x^{10} - 3 x^{9} + 554 x^{8} - 1324 x^{7} + 124330 x^{6} - 222024 x^{5} + 14123866 x^{4} - 16760549 x^{3} + 812086354 x^{2} - 480472389 x + 18909114223$ | $-\,3^{5}\cdot 11^{8}\cdot 149^{5}$ | $C_{10}$ (as 10T1) | $[149870]$ |
10.0.384...487.1 | $x^{10} - x^{9} + 760 x^{8} - 760 x^{7} + 210244 x^{6} - 210244 x^{5} + 25505437 x^{4} - 25505437 x^{3} + 1272197092 x^{2} - 1272197092 x + 18476541931$ | $-\,11^{9}\cdot 277^{5}$ | $C_{10}$ (as 10T1) | $[178258]$ |
10.0.404...192.1 | $x^{10} - 2 x^{9} + 558 x^{8} - 890 x^{7} + 126350 x^{6} - 151226 x^{5} + 14506927 x^{4} - 11621572 x^{3} + 844401882 x^{2} - 340728680 x + 19932627769$ | $-\,2^{10}\cdot 11^{8}\cdot 113^{5}$ | $C_{10}$ (as 10T1) | $[141608]$ |
10.0.405...000.1 | $x^{10} + 770 x^{8} + 215600 x^{6} + 26411000 x^{4} + 1320550000 x^{2} + 18487700000$ | $-\,2^{15}\cdot 5^{5}\cdot 7^{5}\cdot 11^{9}$ | $C_{10}$ (as 10T1) | $[2, 2, 33128]$ |
10.0.422...656.1 | $x^{10} - 2 x^{9} + 563 x^{8} - 898 x^{7} + 128608 x^{6} - 153932 x^{5} + 14894771 x^{4} - 11932126 x^{3} + 874423551 x^{2} - 352816098 x + 20816149771$ | $-\,2^{15}\cdot 3^{5}\cdot 11^{8}\cdot 19^{5}$ | $C_{10}$ (as 10T1) | $[2, 66524]$ |
10.0.435...984.1 | $x^{10} + 781 x^{8} + 221804 x^{6} + 27559147 x^{4} + 1397642455 x^{2} + 19846522861$ | $-\,2^{10}\cdot 11^{9}\cdot 71^{5}$ | $C_{10}$ (as 10T1) | $[10, 17050]$ |
10.0.443...375.1 | $x^{10} - x^{9} + 782 x^{8} - 782 x^{7} + 222586 x^{6} - 222586 x^{5} + 27781733 x^{4} - 27781733 x^{3} + 1425424188 x^{2} - 1425424188 x + 21271947049$ | $-\,3^{5}\cdot 5^{5}\cdot 11^{9}\cdot 19^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 45550]$ |
10.0.456...383.1 | $x^{10} - 3 x^{9} + 574 x^{8} - 1372 x^{7} + 133410 x^{6} - 238304 x^{5} + 15688994 x^{4} - 18624933 x^{3} + 933456526 x^{2} - 552543269 x + 22481787043$ | $-\,11^{8}\cdot 463^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 13454]$ |
10.0.476...267.1 | $x^{10} - 3 x^{9} + 579 x^{8} - 1384 x^{7} + 135730 x^{6} - 242464 x^{5} + 16097556 x^{4} - 19111689 x^{3} + 965814059 x^{2} - 571761689 x + 23454226223$ | $-\,11^{8}\cdot 467^{5}$ | $C_{10}$ (as 10T1) | $[129647]$ |
10.0.496...231.1 | $x^{10} - 3 x^{9} + 584 x^{8} - 1396 x^{7} + 138070 x^{6} - 246660 x^{5} + 16513150 x^{4} - 19606853 x^{3} + 999005584 x^{2} - 591477129 x + 24460026361$ | $-\,3^{5}\cdot 11^{8}\cdot 157^{5}$ | $C_{10}$ (as 10T1) | $[127856]$ |
10.0.502...792.1 | $x^{10} - 2 x^{9} + 583 x^{8} - 930 x^{7} + 137840 x^{6} - 164996 x^{5} + 16515267 x^{4} - 13229662 x^{3} + 1002584407 x^{2} - 404409370 x + 24668971559$ | $-\,2^{15}\cdot 11^{8}\cdot 59^{5}$ | $C_{10}$ (as 10T1) | $[5, 26430]$ |
10.0.509...863.1 | $x^{10} - x^{9} + 804 x^{8} - 804 x^{7} + 235280 x^{6} - 235280 x^{5} + 30189589 x^{4} - 30189589 x^{3} + 1592092844 x^{2} - 1592092844 x + 24395880367$ | $-\,11^{9}\cdot 293^{5}$ | $C_{10}$ (as 10T1) | $[100650]$ |
10.0.540...519.1 | $x^{10} - 3 x^{9} + 594 x^{8} - 1420 x^{7} + 142810 x^{6} - 255160 x^{5} + 17365674 x^{4} - 20622693 x^{3} + 1067947562 x^{2} - 632433125 x + 26575128119$ | $-\,11^{8}\cdot 479^{5}$ | $C_{10}$ (as 10T1) | $[11, 11, 1375]$ |
10.0.563...483.1 | $x^{10} - 3 x^{9} + 599 x^{8} - 1432 x^{7} + 145210 x^{6} - 259464 x^{5} + 17802724 x^{4} - 21143513 x^{3} + 1103726791 x^{2} - 653690889 x + 27686175043$ | $-\,3^{5}\cdot 7^{5}\cdot 11^{8}\cdot 23^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 2, 10, 710]$ |
10.0.582...191.1 | $x^{10} - x^{9} + 826 x^{8} - 826 x^{7} + 248326 x^{6} - 248326 x^{5} + 32732701 x^{4} - 32732701 x^{3} + 1772967076 x^{2} - 1772967076 x + 27876482701$ | $-\,7^{5}\cdot 11^{9}\cdot 43^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 2, 2, 5436]$ |
10.0.587...367.1 | $x^{10} - 3 x^{9} + 604 x^{8} - 1444 x^{7} + 147630 x^{6} - 263804 x^{5} + 18247046 x^{4} - 21673029 x^{3} + 1140397564 x^{2} - 675480089 x + 28834073773$ | $-\,11^{8}\cdot 487^{5}$ | $C_{10}$ (as 10T1) | $[19, 5453]$ |
10.0.593...008.1 | $x^{10} - 2 x^{9} + 603 x^{8} - 962 x^{7} + 147392 x^{6} - 176444 x^{5} + 18249235 x^{4} - 14618014 x^{3} + 1144342191 x^{2} - 461464274 x + 29072249251$ | $-\,2^{15}\cdot 11^{8}\cdot 61^{5}$ | $C_{10}$ (as 10T1) | $[110050]$ |
10.0.611...331.1 | $x^{10} - 3 x^{9} + 609 x^{8} - 1456 x^{7} + 150070 x^{6} - 268180 x^{5} + 18698700 x^{4} - 22211313 x^{3} + 1177974569 x^{2} - 697809509 x + 30019733501$ | $-\,11^{8}\cdot 491^{5}$ | $C_{10}$ (as 10T1) | $[119295]$ |
10.0.622...875.1 | $x^{10} - x^{9} + 837 x^{8} - 837 x^{7} + 254981 x^{6} - 254981 x^{5} + 34056133 x^{4} - 34056133 x^{3} + 1868975813 x^{2} - 1868975813 x + 29759754949$ | $-\,5^{5}\cdot 11^{9}\cdot 61^{5}$ | $C_{10}$ (as 10T1) | $[2, 65924]$ |
10.0.663...619.1 | $x^{10} - 3 x^{9} + 619 x^{8} - 1480 x^{7} + 155010 x^{6} - 277040 x^{5} + 19624244 x^{4} - 23314473 x^{3} + 1255906627 x^{2} - 744124505 x + 32508046999$ | $-\,11^{8}\cdot 499^{5}$ | $C_{10}$ (as 10T1) | $[134013]$ |
10.0.664...359.1 | $x^{10} - x^{9} + 848 x^{8} - 848 x^{7} + 261724 x^{6} - 261724 x^{5} + 35414765 x^{4} - 35414765 x^{3} + 1968832020 x^{2} - 1968832020 x + 31743457747$ | $-\,3^{5}\cdot 11^{9}\cdot 103^{5}$ | $C_{10}$ (as 10T1) | $[2, 67100]$ |
10.0.690...583.1 | $x^{10} - 3 x^{9} + 624 x^{8} - 1492 x^{7} + 157510 x^{6} - 281524 x^{5} + 20098254 x^{4} - 23879493 x^{3} + 1296291656 x^{2} - 768128009 x + 33812593793$ | $-\,11^{8}\cdot 503^{5}$ | $C_{10}$ (as 10T1) | $[5, 45255]$ |
10.0.697...912.1 | $x^{10} + 858 x^{8} + 267696 x^{6} + 36540504 x^{4} + 2035828080 x^{2} + 31758918048$ | $-\,2^{15}\cdot 3^{5}\cdot 11^{9}\cdot 13^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 40804]$ |
10.0.708...963.1 | $x^{10} - x^{9} + 859 x^{8} - 859 x^{7} + 268555 x^{6} - 268555 x^{5} + 36809059 x^{4} - 36809059 x^{3} + 2072637139 x^{2} - 2072637139 x + 33831555187$ | $-\,11^{9}\cdot 313^{5}$ | $C_{10}$ (as 10T1) | $[118096]$ |
10.0.742...016.1 | $x^{10} + 869 x^{8} + 274604 x^{6} + 37964003 x^{4} + 2142254455 x^{2} + 33847620389$ | $-\,2^{10}\cdot 11^{9}\cdot 79^{5}$ | $C_{10}$ (as 10T1) | $[2, 64016]$ |
10.0.746...431.1 | $x^{10} - 3 x^{9} + 634 x^{8} - 1516 x^{7} + 162570 x^{6} - 290600 x^{5} + 21069050 x^{4} - 25036773 x^{3} + 1379975554 x^{2} - 817872389 x + 36547313791$ | $-\,7^{5}\cdot 11^{8}\cdot 73^{5}$ | $C_{10}$ (as 10T1) | $[161714]$ |
10.0.754...687.1 | $x^{10} - x^{9} + 870 x^{8} - 870 x^{7} + 275474 x^{6} - 275474 x^{5} + 38239477 x^{4} - 38239477 x^{3} + 2180493932 x^{2} - 2180493932 x + 36028114321$ | $-\,11^{9}\cdot 317^{5}$ | $C_{10}$ (as 10T1) | $[180628]$ |
10.0.776...875.1 | $x^{10} - 3 x^{9} + 639 x^{8} - 1528 x^{7} + 165130 x^{6} - 295192 x^{5} + 21565956 x^{4} - 25629177 x^{3} + 1423305119 x^{2} - 843631625 x + 37979471531$ | $-\,5^{5}\cdot 11^{8}\cdot 103^{5}$ | $C_{10}$ (as 10T1) | $[130506]$ |
10.0.784...456.1 | $x^{10} - 2 x^{9} + 638 x^{8} - 1018 x^{7} + 164878 x^{6} - 197402 x^{5} + 21568271 x^{4} - 17275396 x^{3} + 1427948346 x^{2} - 575579688 x + 38276049241$ | $-\,2^{10}\cdot 3^{5}\cdot 11^{8}\cdot 43^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 2, 2, 6330]$ |
10.0.803...291.1 | $x^{10} - x^{9} + 881 x^{8} - 881 x^{7} + 282481 x^{6} - 282481 x^{5} + 39706481 x^{4} - 39706481 x^{3} + 2292506481 x^{2} - 2292506481 x + 38337306481$ | $-\,3^{5}\cdot 11^{9}\cdot 107^{5}$ | $C_{10}$ (as 10T1) | $[22, 6248]$ |
10.0.807...719.1 | $x^{10} - 3 x^{9} + 644 x^{8} - 1540 x^{7} + 167710 x^{6} - 299820 x^{5} + 22070614 x^{4} - 26230853 x^{3} + 1467647092 x^{2} - 869994585 x + 39456176629$ | $-\,3^{5}\cdot 11^{8}\cdot 173^{5}$ | $C_{10}$ (as 10T1) | $[162090]$ |
10.0.815...000.1 | $x^{10} - 2 x^{9} + 643 x^{8} - 1026 x^{7} + 167456 x^{6} - 200492 x^{5} + 22072947 x^{4} - 17679454 x^{3} + 1472396383 x^{2} - 593461186 x + 39761899451$ | $-\,2^{15}\cdot 5^{5}\cdot 11^{8}\cdot 13^{5}$ | $C_{10}$ (as 10T1) | $[2, 89122]$ |
10.0.838...683.2 | $x^{10} - 3 x^{9} + 649 x^{8} - 1552 x^{7} + 170310 x^{6} - 304484 x^{5} + 22583084 x^{4} - 26841873 x^{3} + 1513017121 x^{2} - 896970629 x + 40978460293$ | $-\,11^{8}\cdot 523^{5}$ | $C_{10}$ (as 10T1) | $[5, 49775]$ |
10.0.871...567.1 | $x^{10} - 3 x^{9} + 654 x^{8} - 1564 x^{7} + 172930 x^{6} - 309184 x^{5} + 23103426 x^{4} - 27462309 x^{3} + 1559430974 x^{2} - 924569189 x + 42547369523$ | $-\,11^{8}\cdot 17^{5}\cdot 31^{5}$ | $C_{10}$ (as 10T1) | $[198090]$ |
10.0.895...288.1 | $x^{10} + 902 x^{8} + 295856 x^{6} + 42455336 x^{4} + 2486669680 x^{2} + 40781382752$ | $-\,2^{15}\cdot 11^{9}\cdot 41^{5}$ | $C_{10}$ (as 10T1) | $[2, 120274]$ |
10.0.908...459.1 | $x^{10} - x^{9} + 903 x^{8} - 903 x^{7} + 296759 x^{6} - 296759 x^{5} + 42752095 x^{4} - 42752095 x^{3} + 2529421775 x^{2} - 2529421775 x + 43310804527$ | $-\,7^{5}\cdot 11^{9}\cdot 47^{5}$ | $C_{10}$ (as 10T1) | $[2, 69726]$ |
10.0.913...592.1 | $x^{10} - 2 x^{9} + 658 x^{8} - 1050 x^{7} + 175310 x^{6} - 209906 x^{5} + 23634087 x^{4} - 18929332 x^{3} + 1611981682 x^{2} - 649611640 x + 44498397329$ | $-\,2^{10}\cdot 7^{5}\cdot 11^{8}\cdot 19^{5}$ | $C_{10}$ (as 10T1) | $[2, 60302]$ |
10.0.939...375.1 | $x^{10} - 3 x^{9} + 664 x^{8} - 1588 x^{7} + 178230 x^{6} - 318692 x^{5} + 24167966 x^{4} - 28731717 x^{3} + 1655453824 x^{2} - 981671945 x + 45829332361$ | $-\,5^{5}\cdot 11^{8}\cdot 107^{5}$ | $C_{10}$ (as 10T1) | $[185570]$ |
10.0.948...056.1 | $x^{10} - 2 x^{9} + 663 x^{8} - 1058 x^{7} + 177968 x^{6} - 213092 x^{5} + 24170371 x^{4} - 19358686 x^{3} + 1660643511 x^{2} - 669185018 x + 46173766231$ | $-\,2^{15}\cdot 11^{8}\cdot 67^{5}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 2, 17570]$ |
10.0.951...512.1 | $x^{10} + 913 x^{8} + 303116 x^{6} + 44027599 x^{4} + 2610207655 x^{2} + 43329447073$ | $-\,2^{10}\cdot 11^{9}\cdot 83^{5}$ | $C_{10}$ (as 10T1) | $[2, 52086]$ |
10.0.101...783.1 | $x^{10} - 3 x^{9} + 674 x^{8} - 1612 x^{7} + 183610 x^{6} - 328344 x^{5} + 25264714 x^{4} - 30039653 x^{3} + 1755844186 x^{2} - 1041379749 x + 49310761543$ | $-\,3^{5}\cdot 11^{8}\cdot 181^{5}$ | $C_{10}$ (as 10T1) | $[240852]$ |