LMFDB - Global number field search results

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Results (displaying all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
45.1.246012870627780535441003976786240313709044401656133556774425683161984460829.1	x⁴⁵ - x - 1	$ 29\cdot 41\cdot 1451\cdot 23184662326519\cdot 476883331418375569\cdot 12897206214339827420730516506448469501 $	$S_{45}$ (as 45T10923)	n/a
45.1.4219671405487469795007840774828326879559861579577302862304338876222359629344736024723456.1	x⁴⁵ - 4x - 4	$ 2^{44}\cdot 61\cdot 6357179\cdot 171802225249\cdot 418161846581\cdot 8092657633001\cdot 14050885843711\cdot 75717538318411921 $	$S_{45}$ (as 45T10923)	n/a
45.1.4291826594765663003976769757283345274790293039788651431152169438111179814672368012361728.1	x⁴⁵ - 2x - 2	$ 2^{44}\cdot 79\cdot 1013\cdot 3048497342199756649472787573907155555919354990435889752547649745658279 $	$S_{45}$ (as 45T10923)	n/a
45.1.4363981784043854162171875179128310024815115327623964513820163479392452705083033810632704.1	x⁴⁵ - x - 2	$ 2^{44}\cdot 248063644451341028921653740958863069455169086701514772461232694206072023069 $	$S_{45}$ (as 45T10923)	n/a
45.1.4508292162600242630883556704648400460481587420422697137695661123777640370655263975276544.1	x⁴⁵ + 4x - 4	$ 2^{44}\cdot 523\cdot 326083\cdot 86999456098802843\cdot 17272128465413103990048781624806825473342473446407 $	$S_{45}$ (as 45T10923)	n/a
45.1.461788013129114908410483449590003725369038828566163185526779909482248505594982451554016695549.1	x⁴⁵ + x - 3	$ 41\cdot 281\cdot 2689\cdot 3061\cdot 9790127\cdot 497404856720178834753693302562002159288580122855457096966807286973147607143 $	$S_{45}$ (as 45T10923)	n/a
45.3.6058627165206947772659446834243918770516708613809690476129633884301485702351604141067529951203.1	x⁴⁵ - 3x - 1	$ -\,3^{45}\cdot 66012539\cdot 28278051239\cdot 68372307116461\cdot 16067992358028006974094700413220621293241 $	$S_{45}$ (as 45T10923)	n/a
45.1.6058627165206947773155574123146601061506006978600515855618695047286794030995045341323877607453.1	x⁴⁵ + 3x - 1	$ 3^{45}\cdot 991\cdot 5482500513935539\cdot 377455214821004106697105676903957430884841884160251179 $	$S_{45}$ (as 45T10923)	n/a
45.1.6058631529188731816763723424393999654375027816929603165874164465794139866673324741195703779328.1	x⁴⁵ + 3x - 2	$ 2^{44}\cdot 3^{45}\cdot 8431\cdot 40996793\cdot 141817543613\cdot 2378150503072556132510163888173917789 $	$S_{45}$ (as 45T10923)	n/a
45.1.244285858873146597270950485090359427655149499875459692556282517088442376963378236627476654939853.1	x⁴⁵ - 2x - 3	$ 1294351\cdot 15211842839\cdot 12406932915542118318333796429503421775022365907034043080317641893056767027113877 $	$S_{45}$ (as 45T10923)	n/a
45.1.244285858945301786549141643285464849500114249900281980391595599756436418244651127038142453210829.1	x⁴⁵ - x - 3	$ 394759\cdot 17295724778674525629079\cdot 35778944257145220698016100371727896939679299851967974758576839513389 $	$S_{45}$ (as 45T10923)	n/a
45.3.2538735027699687144412949043193794155334981938018953417004197950355756515384020435188568211066978304.1	x⁴⁵ - 4x - 2	$ -\,2^{44}\cdot 2834789\cdot 50906920605427195566727055793056252609442010581017707883785519702989763984245671 $	$S_{45}$ (as 45T10923)	n/a
45.1.2538735027704051126196993147470384305415865796338156536916887694886338008038184756909168339240806429.1	x⁴⁵ + 4x - 1	$ 41\cdot 547\cdot 107899001480198069\cdot 1049128696814844200913942061815894663458796386336770071320289318330982069823083 $	$S_{45}$ (as 45T10923)	n/a
45.1.2538735027708415107981036755619685552814458665358994866004197950355756515384020435188568211066978304.1	x⁴⁵ + 4x - 2	$ 2^{44}\cdot 7\cdot 2687\cdot 7672411003064197011128146422219758607223049237728835572181071717898989380370681541 $	$S_{45}$ (as 45T10923)	n/a
45.1.19192994859835473355074744872607517828470978752000567240134947162857788042359527794953668092003090432.1	x⁴⁵ - 2x - 4	$ 2^{86}\cdot 166289\cdot 17194056911\cdot 97370596099401809\cdot 891032222208071115812369072217086199036083 $	$S_{45}$ (as 45T10923)	n/a
45.1.19192994859835509432669383969212002292962206261198182455865052837142211957640472205046331907996909568.1	x⁴⁵ + 2x - 4	$ 2^{86}\cdot 59\cdot 4204468550022735231197289241839185259716162221609033017672820541904702343 $	$S_{45}$ (as 45T10923)	n/a
45.1.76771973380714800368540484776128561547606454015039703186896834125835534205860133326675258804296220672.1	x⁴⁵ - 3x - 4	$ 2^{89}\cdot 3^{45}\cdot 61\cdot 1183211\cdot 1595562959\cdot 364561370664661220582384110700994703 $	$S_{45}$ (as 45T10923)	n/a
45.3.1189520361647311641758426463337537892861867432950966956771500000000000000000000000000000000000000000000.1	x⁴⁵ - 5x - 2	$ -\,2^{44}\cdot 5^{45}\cdot 73\cdot 44175746519\cdot 6490952564449\cdot 14705222713099\cdot 7728853529686445339 $	$S_{45}$ (as 45T10923)	n/a
45.3.2331459899057296634593715767930075025465673353711726231865473889294756562549082445912063121795654296875.1	x⁴⁵ - 5x - 3	$ -\,5^{43}\cdot 157\cdot 1531\cdot 4729\cdot 4801\cdot 15817\cdot 31873\cdot 97849\cdot 18359951437\cdot 35107655355337\cdot 11818574496687068323309 $	$S_{45}$ (as 45T10923)	n/a
45.1.14571624430179569793531616197812945660407245922831180230813125000000000000000000000000000000000000000000.1	x⁴⁵ + 5x - 2	$ 2^{42}\cdot 5^{46}\cdot 53\cdot 22846124160878734429091761\cdot 19254823833912889768262197122097 $	$S_{45}$ (as 45T10923)	n/a
45.3.58286497720718274810144680747147506051478902807466401720132587310255469418507345835678279399871826171875.1	x⁴⁵ - 5x - 1	$ -\,5^{45}\cdot 13\cdot 47\cdot 241\cdot 313\cdot 10159\cdot 1560681193\cdot 441481146991\cdot 24561359840613046207\cdot 258812619101427272051 $	$S_{45}$ (as 45T10923)	n/a
45.1.58286497720718274810144680747643633340381585098455700084923412689744530581492654164321720600128173828125.1	x⁴⁵ + 5x - 1	$ 5^{46}\cdot 101\cdot 677\cdot 119549\cdot 842977\cdot 818961053\cdot 72679644912024426232556982099430424324466270773 $	$S_{45}$ (as 45T10923)	n/a
45.1.58286497965004133755446467296539263755218654063128946008419152767631085936272938852198421955108642578125.1	x⁴⁵ + 5x - 3	$ 5^{46}\cdot 29\cdot 699023939659537\cdot 20232880457368282662668714658655455158647688849895180601 $	$S_{45}$ (as 45T10923)	n/a
45.1.58363269700157616775720169005079208736173110322987448401920000000000000000000000000000000000000000000000.1	x⁴⁵ + 5x - 4	$ 2^{89}\cdot 5^{46}\cdot 149\cdot 4453111121681026051225605378891768357546101 $	$S_{45}$ (as 45T10923)	n/a

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Results (displaying all 24 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
45.1.246012870627780535441003976786240313709044401656133556774425683161984460829.1	x⁴⁵ - x - 1	\( 29\cdot 41\cdot 1451\cdot 23184662326519\cdot 476883331418375569\cdot 12897206214339827420730516506448469501 \)	$S_{45}$ (as 45T10923)	n/a
45.1.4219671405487469795007840774828326879559861579577302862304338876222359629344736024723456.1	x⁴⁵ - 4x - 4	\( 2^{44}\cdot 61\cdot 6357179\cdot 171802225249\cdot 418161846581\cdot 8092657633001\cdot 14050885843711\cdot 75717538318411921 \)	$S_{45}$ (as 45T10923)	n/a
45.1.4291826594765663003976769757283345274790293039788651431152169438111179814672368012361728.1	x⁴⁵ - 2x - 2	\( 2^{44}\cdot 79\cdot 1013\cdot 3048497342199756649472787573907155555919354990435889752547649745658279 \)	$S_{45}$ (as 45T10923)	n/a
45.1.4363981784043854162171875179128310024815115327623964513820163479392452705083033810632704.1	x⁴⁵ - x - 2	\( 2^{44}\cdot 248063644451341028921653740958863069455169086701514772461232694206072023069 \)	$S_{45}$ (as 45T10923)	n/a
45.1.4508292162600242630883556704648400460481587420422697137695661123777640370655263975276544.1	x⁴⁵ + 4x - 4	\( 2^{44}\cdot 523\cdot 326083\cdot 86999456098802843\cdot 17272128465413103990048781624806825473342473446407 \)	$S_{45}$ (as 45T10923)	n/a
45.1.461788013129114908410483449590003725369038828566163185526779909482248505594982451554016695549.1	x⁴⁵ + x - 3	\( 41\cdot 281\cdot 2689\cdot 3061\cdot 9790127\cdot 497404856720178834753693302562002159288580122855457096966807286973147607143 \)	$S_{45}$ (as 45T10923)	n/a
45.3.6058627165206947772659446834243918770516708613809690476129633884301485702351604141067529951203.1	x⁴⁵ - 3x - 1	\( -\,3^{45}\cdot 66012539\cdot 28278051239\cdot 68372307116461\cdot 16067992358028006974094700413220621293241 \)	$S_{45}$ (as 45T10923)	n/a
45.1.6058627165206947773155574123146601061506006978600515855618695047286794030995045341323877607453.1	x⁴⁵ + 3x - 1	\( 3^{45}\cdot 991\cdot 5482500513935539\cdot 377455214821004106697105676903957430884841884160251179 \)	$S_{45}$ (as 45T10923)	n/a
45.1.6058631529188731816763723424393999654375027816929603165874164465794139866673324741195703779328.1	x⁴⁵ + 3x - 2	\( 2^{44}\cdot 3^{45}\cdot 8431\cdot 40996793\cdot 141817543613\cdot 2378150503072556132510163888173917789 \)	$S_{45}$ (as 45T10923)	n/a
45.1.244285858873146597270950485090359427655149499875459692556282517088442376963378236627476654939853.1	x⁴⁵ - 2x - 3	\( 1294351\cdot 15211842839\cdot 12406932915542118318333796429503421775022365907034043080317641893056767027113877 \)	$S_{45}$ (as 45T10923)	n/a
45.1.244285858945301786549141643285464849500114249900281980391595599756436418244651127038142453210829.1	x⁴⁵ - x - 3	\( 394759\cdot 17295724778674525629079\cdot 35778944257145220698016100371727896939679299851967974758576839513389 \)	$S_{45}$ (as 45T10923)	n/a
45.3.2538735027699687144412949043193794155334981938018953417004197950355756515384020435188568211066978304.1	x⁴⁵ - 4x - 2	\( -\,2^{44}\cdot 2834789\cdot 50906920605427195566727055793056252609442010581017707883785519702989763984245671 \)	$S_{45}$ (as 45T10923)	n/a
45.1.2538735027704051126196993147470384305415865796338156536916887694886338008038184756909168339240806429.1	x⁴⁵ + 4x - 1	\( 41\cdot 547\cdot 107899001480198069\cdot 1049128696814844200913942061815894663458796386336770071320289318330982069823083 \)	$S_{45}$ (as 45T10923)	n/a
45.1.2538735027708415107981036755619685552814458665358994866004197950355756515384020435188568211066978304.1	x⁴⁵ + 4x - 2	\( 2^{44}\cdot 7\cdot 2687\cdot 7672411003064197011128146422219758607223049237728835572181071717898989380370681541 \)	$S_{45}$ (as 45T10923)	n/a
45.1.19192994859835473355074744872607517828470978752000567240134947162857788042359527794953668092003090432.1	x⁴⁵ - 2x - 4	\( 2^{86}\cdot 166289\cdot 17194056911\cdot 97370596099401809\cdot 891032222208071115812369072217086199036083 \)	$S_{45}$ (as 45T10923)	n/a
45.1.19192994859835509432669383969212002292962206261198182455865052837142211957640472205046331907996909568.1	x⁴⁵ + 2x - 4	\( 2^{86}\cdot 59\cdot 4204468550022735231197289241839185259716162221609033017672820541904702343 \)	$S_{45}$ (as 45T10923)	n/a
45.1.76771973380714800368540484776128561547606454015039703186896834125835534205860133326675258804296220672.1	x⁴⁵ - 3x - 4	\( 2^{89}\cdot 3^{45}\cdot 61\cdot 1183211\cdot 1595562959\cdot 364561370664661220582384110700994703 \)	$S_{45}$ (as 45T10923)	n/a
45.3.1189520361647311641758426463337537892861867432950966956771500000000000000000000000000000000000000000000.1	x⁴⁵ - 5x - 2	\( -\,2^{44}\cdot 5^{45}\cdot 73\cdot 44175746519\cdot 6490952564449\cdot 14705222713099\cdot 7728853529686445339 \)	$S_{45}$ (as 45T10923)	n/a
45.3.2331459899057296634593715767930075025465673353711726231865473889294756562549082445912063121795654296875.1	x⁴⁵ - 5x - 3	\( -\,5^{43}\cdot 157\cdot 1531\cdot 4729\cdot 4801\cdot 15817\cdot 31873\cdot 97849\cdot 18359951437\cdot 35107655355337\cdot 11818574496687068323309 \)	$S_{45}$ (as 45T10923)	n/a
45.1.14571624430179569793531616197812945660407245922831180230813125000000000000000000000000000000000000000000.1	x⁴⁵ + 5x - 2	\( 2^{42}\cdot 5^{46}\cdot 53\cdot 22846124160878734429091761\cdot 19254823833912889768262197122097 \)	$S_{45}$ (as 45T10923)	n/a
45.3.58286497720718274810144680747147506051478902807466401720132587310255469418507345835678279399871826171875.1	x⁴⁵ - 5x - 1	\( -\,5^{45}\cdot 13\cdot 47\cdot 241\cdot 313\cdot 10159\cdot 1560681193\cdot 441481146991\cdot 24561359840613046207\cdot 258812619101427272051 \)	$S_{45}$ (as 45T10923)	n/a
45.1.58286497720718274810144680747643633340381585098455700084923412689744530581492654164321720600128173828125.1	x⁴⁵ + 5x - 1	\( 5^{46}\cdot 101\cdot 677\cdot 119549\cdot 842977\cdot 818961053\cdot 72679644912024426232556982099430424324466270773 \)	$S_{45}$ (as 45T10923)	n/a
45.1.58286497965004133755446467296539263755218654063128946008419152767631085936272938852198421955108642578125.1	x⁴⁵ + 5x - 3	\( 5^{46}\cdot 29\cdot 699023939659537\cdot 20232880457368282662668714658655455158647688849895180601 \)	$S_{45}$ (as 45T10923)	n/a
45.1.58363269700157616775720169005079208736173110322987448401920000000000000000000000000000000000000000000000.1	x⁴⁵ + 5x - 4	\( 2^{89}\cdot 5^{46}\cdot 149\cdot 4453111121681026051225605378891768357546101 \)	$S_{45}$ (as 45T10923)	n/a