LMFDB - Global number field search results

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Results (displaying all 42 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)
31.1.18770034004737848533180532351835033630345588173537542144.1	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)
31.1.3514391585695303498411406095396469962323789296982843961159719.1	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
31.1.15896907197985086551505014396253074975127944915555417537689208984375.1	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

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Further refine search

Results (displaying all 42 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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)
31.1.18770034004737848533180532351835033630345588173537542144.1	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)
31.1.3514391585695303498411406095396469962323789296982843961159719.1	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
31.1.15896907197985086551505014396253074975127944915555417537689208984375.1	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