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Results (displaying all 49 matches)

Label Polynomial Discriminant Galois group Class group
31.1.16863282998628586958610643029059314756044734431.1 x31 - x - 1 \( -\,4211\cdot 107951341831\cdot 1040542609867\cdot 35650774802780191673 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.17275065262817884958610643029059314756044734431.1 x31 + x - 1 \( -\,107\cdot 349\cdot 462605180698333957063188362720170172617217 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.3654114516616866500188330236451595281481940132601111.1 x31 + 2x - 1 \( -\,71\cdot 6073\cdot 8474625661533192403662320259499088047260537017 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.17443590486413448385781876351835033630345588173537542144.1 x31 - 4x - 4 \( -\,2^{30}\cdot 29161973\cdot 14898732471895043\cdot 37391233052164359356929 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.17885738325854915101581428351835033630345588173537542144.1 x31 - 2x - 2 \( -\,2^{30}\cdot 937\cdot 17777365919459912442487345815431499206024263 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.18327886165090490685286331351835033630345588173537542144.1 x31 - x - 2 \( -\,2^{31}\cdot 1433\cdot 3653617274537267\cdot 1630096334391835835360875373 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.18327886165296381817189229292602149543677096810012151519.1 x31 - x - 4 \( -\,23\cdot 1693\cdot 3697\cdot 19843\cdot 14132537\cdot 75771043\cdot 5991663366536301415229073661 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.18327886165296381817380980351835033630345588173537542144.1 x31 - 2 \( -\,2^{30}\cdot 31^{31} \) $F_{31}$ (as 31T8) Trivial (GRH)
31.1.18770034004737848533180532351835033630345588173537542144.1 x31 + 2x - 2 \( -\,2^{30}\cdot 11\cdot 1489\cdot 1499\cdot 23334601\cdot 28850169461\cdot 1057614572100224186051 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.19212181844179315248980084351835033630345588173537542144.1 x31 + 4x - 4 \( -\,2^{30}\cdot 7\cdot 90373\cdot 161611\cdot 54687761\cdot 3200213985295117341572815151 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.3.127173474825631541368752576367041389356970940685243955265569.1 x31 - 3x - 1 \( 7\cdot 17\cdot 23\cdot 15726392777460683\cdot 2954558696113433838143509264321373433139 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.127173474825665679717014022838958610643029059314756044734431.1 x31 + 3x - 1 \( -\,43\cdot 39047\cdot 455317\cdot 317197259\cdot 45044106017368643\cdot 11642845821394330173359 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.127191802711813906924700680583351835033630345588173537542144.1 x31 + 3x - 2 \( -\,2^{31}\cdot 59\cdot 316799009\cdot 3168789797431193875936087552428199953263 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.3387218110869654681977390701144469962323789296982843961159719.1 x31 - 3x - 3 \( -\,3^{30}\cdot 7\cdot 2713\cdot 14387\cdot 3413878991\cdot 72413150415649\cdot 243568924508677 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.3514391143547463851053558201195469962323789296982843961159719.1 x31 - 2x - 3 \( -\,3^{30}\cdot 1069\cdot 745011551\cdot 21432446223951881420287139805088549 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.3514391585695303086629141906098469962323789296982843961159719.1 x31 - x - 3 \( -\,3^{31}\cdot 571\cdot 9964491611630610016702068318189909373055887 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.3514391585695303292520274000747469962323789296982843961159719.1 x31 - 3 \( -\,3^{30}\cdot 31^{31} \) $F_{31}$ (as 31T8) Trivial (GRH)
31.1.3514391585695303498411406095396469962323789296982843961159719.1 x31 + x - 3 \( -\,3^{30}\cdot 19\cdot 3539\cdot 253850688281305110849193840499982373195591 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.3641565060520951903063157300350469962323789296982843961159719.1 x31 + 3x - 3 \( -\,3^{30}\cdot 678106210770691935341\cdot 26082709826393492021802491 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.19449380546628051604251457953600887142088240597897609060431831.1 x31 + 4x - 3 \( -\,3^{30}\cdot 59\cdot 10709\cdot 149508953636113788369933546329314530107849 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.3.949505236871193060019419348344715648164966369654411826462457856.1 x31 - 4x - 2 \( 2^{30}\cdot 2383\cdot 371085044823230927769982392525957604255428134265743 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.3.949505255199079208246627035002460041389356970940685243955265569.1 x31 - 4x - 1 \( 24365060088671\cdot 38969953357125920236474466375786993070484887309439 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.949505255199079242384975296448931958610643029059314756044734431.1 x31 + 4x - 1 \( -\,7\cdot 135643607885582748912139328064133136944377575579902108006390633 \) $S_{31}$ (as 31T12) $[2]$ (GRH)
31.1.949505273526965390612182983106676351835033630345588173537542144.1 x31 + 4x - 2 \( -\,2^{30}\cdot 7\cdot 195469\cdot 212031575390627\cdot 3048042651910299213783523530349391 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.4919854480186888668438405507521989689337153398951757258543857664.1 x31 - 2x - 4 \( -\,2^{58}\cdot 18637\cdot 915875630752789281544501521474611366045713 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.4919854480407962588159138865421765689337153398951757258543857664.1 x31 + 2x - 4 \( -\,2^{58}\cdot 11\cdot 1551743102827885279734219200217845225735955971 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.19679290747714876864584545862587907757348613595807029034175430656.1 x31 - 3x - 4 \( -\,2^{30}\cdot 7\cdot 81987621103882733\cdot 1994715371164304797\cdot 16009667507940703067 \) $S_{31}$ (as 31T12) n/a
31.1.19679417921189702513400979877982159757348613595807029034175430656.1 x31 + x - 4 \( -\,2^{30}\cdot 103\cdot 1946342156463328037\cdot 91423104509461892642018507223348779 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.106528756728445125405083259766772652496662480421032998093773462191.1 x31 + 5x - 3 \( -\,3^{30}\cdot 43\cdot 16293623473\cdot 738487392300001178494609875436847461381 \) $S_{31}$ (as 31T12) n/a
31.1.239688824045687079876938299861083526337958758407586397043384385536.1 x31 + 5x - 2 \( -\,2^{30}\cdot 13\cdot 17\cdot 27768997\cdot 113656553679773909591\cdot 320037570123859568648600917 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.3.958751781772834738039164297352952377530037676210703017156038840281.1 x31 - 5x - 3 \( 3^{30}\cdot 13\cdot 16690100963\cdot 21461804096776561542209810433141867740951 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.3.958755296146092547177160435809572144648164966369654411826462457856.1 x31 - 5x - 2 \( 2^{31}\cdot 15619263033943\cdot 55942004669294094613\cdot 510951109592180719533133 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.3.958755296164420433325387643496229889041389356970940685243955265569.1 x31 - 5x - 1 \( 13\cdot 1877\cdot 25841\cdot 202437701896105219\cdot 7511028960944005414303516302480340104011 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.958755296164420433359525991757676360958610643029059314756044734431.1 x31 + 5x - 1 \( -\,59\cdot 18439\cdot 881289102744110386293905412126357417594625469623669170959531 \) $S_{31}$ (as 31T12) n/a
31.1.978434714085610135855651906372840635757348613595807029034175430656.1 x31 + 5x - 4 \( -\,2^{30}\cdot 105767\cdot 8615525986511577652263541855966909992591146411829707 \) $S_{31}$ (as 31T12) n/a
31.1.14938151901820666118162351687494027201127944915555417537689208984375.1 x31 - 5x - 5 \( -\,5^{30}\cdot 443\cdot 26931473971\cdot 1344413583720602215290496879684127 \) $S_{31}$ (as 31T12) n/a
31.1.15895957692729887472279492703955254630127944915555417537689208984375.1 x31 - 4x - 5 \( -\,5^{30}\cdot 139\cdot 162071227763491\cdot 757645147032594015522973305823 \) $S_{31}$ (as 31T12) n/a
31.1.15896907070811611725856197962237680723127944915555417537689208984375.1 x31 - 3x - 5 \( -\,5^{30}\cdot 7\cdot 43132069\cdot 56534580516849828090624310058612141173 \) $S_{31}$ (as 31T12) n/a
31.1.15896907197984644403665367038405180774127944915555417537689208984375.1 x31 - 2x - 5 \( -\,5^{30}\cdot 17069174130722761205983043489446656855461871583 \) $S_{31}$ (as 31T12) n/a
31.1.15896907197985086551504602613988885677127944915555417537689208984375.1 x31 - x - 5 \( -\,5^{31}\cdot 3413834826144647191722084391027918804537366931 \) $S_{31}$ (as 31T12) n/a
31.1.15896907197985086551504808505120980326127944915555417537689208984375.1 x31 - 5 \( -\,5^{30}\cdot 31^{31} \) $F_{31}$ (as 31T8) n/a
31.1.15896907197985086551505014396253074975127944915555417537689208984375.1 x31 + x - 5 \( -\,5^{30}\cdot 19\cdot 173\cdot 2149711\cdot 2415642857167545477712001227465640951 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.15896907197985528699344249971836779878127944915555417537689208984375.1 x31 + 2x - 5 \( -\,5^{30}\cdot 11\cdot 71\cdot 311\cdot 1667\cdot 209394034439\cdot 201326610321383981030559113 \) $S_{31}$ (as 31T12) Trivial (GRH)
31.1.15896907325158561377153419048004279929127944915555417537689208984375.1 x31 + 3x - 5 \( -\,5^{30}\cdot 190717\cdot 89500014509848177049348847226206678434059 \) $S_{31}$ (as 31T12) n/a
31.1.16855662494149506984847265322747933451127944915555417537689208984375.1 x31 + 5x - 5 \( -\,5^{30}\cdot 13\cdot 23\cdot 863\cdot 91923297263327\cdot 763023859796690773329733469 \) $S_{31}$ (as 31T12) n/a
31.31.606473279060866185803408353837168008326030742006308575695635765007438922801.1 x31 - x30 - 150x29 + 117x28 + 9434x27 - 4958x26 - 328880x25 + 78328x24 + 7098810x23 + 507925x22 - 100297691x21 - 39217806x20 + 950942678x19 + 677567200x18 - 6056859921x17 - 6293114670x16 + 25303767350x15 + 35315191500x14 - 65145555320x13 - 122001770825x12 + 87706314807x11 + 253609179978x10 - 19776440614x9 - 299693882286x8 - 98200795275x7 + 175359843704x6 + 113820457794x5 - 30260338943x4 - 38729335872x3 - 5811762482x2 + 1056847214x - 26458109 \( 311^{30} \) $C_{31}$ (as 31T1) n/a
31.31.141665779057617804812220628546407520099809429585876757651733901377160976997449.1 x31 - x30 - 180x29 + 381x28 + 13354x27 - 40454x26 - 531040x25 + 2069355x24 + 12295300x23 - 60883682x22 - 164683595x21 + 1114070344x20 + 1058778882x19 - 13103530537x18 + 1853849258x17 + 99224120479x16 - 91885359548x15 - 467511308511x14 + 762650059488x13 + 1229830733203x12 - 3225889300699x11 - 1095874556276x10 + 7495923118841x9 - 2504773526476x8 - 8920808783994x7 + 7437366186489x6 + 3836259163454x5 - 6642200925120x4 + 1200673450587x3 + 1711910811444x2 - 967097412303x + 151576217389 \( 373^{30} \) $C_{31}$ (as 31T1) Trivial (GRH)
31.31.10780058321499447579019490584061143592974328542534512659762928215062178274195635731849.1 x31 - x30 - 330x29 + 852x28 + 43784x27 - 173944x26 - 2923572x25 + 15562316x24 + 100635650x23 - 707709554x22 - 1616621784x21 + 17266725972x20 + 7046247776x19 - 243865756432x18 + 142454592564x17 + 2084163747748x16 - 2521472241195x15 - 10836712986085x14 + 18499228115810x13 + 32698257976552x12 - 74538290301632x11 - 47884603550112x10 + 168256221920320x9 + 4878741111552x8 - 195294436805376x7 + 62882730299136x6 + 92885896276480x5 - 43440624908288x4 - 15171034030080x3 + 6823763935232x2 + 786648006656x + 5192548352 \( 683^{30} \) $C_{31}$ (as 31T1) Trivial (GRH)
31.31.303180754947920226773910663600827932461415650100367091342054488471568688197420529491484801.1 x31 - 465x29 - 341x28 + 91078x27 + 119908x26 - 9914451x25 - 18008892x24 + 666449563x23 + 1538774528x22 - 28934386579x21 - 83032233092x20 + 817351924162x19 + 2943382779538x18 - 14471455469735x17 - 68751097280499x16 + 137645143880654x15 + 1028543867187214x14 - 144266178422457x13 - 9110738641752719x12 - 11199776062831713x11 + 37846129267859005x10 + 105950708850677777x9 + 9682358886535270x8 - 290542929220278846x7 - 437492517497239584x6 - 201727405103545942x5 + 73256081844015542x4 + 87563225965427030x3 + 7669633084320922x2 - 7522164033404415x - 310695313260929 \( 31^{60} \) $C_{31}$ (as 31T1) n/a



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