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Results (1-50 of 508 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
5.1.471888729.2	$x^{5} - x^{4} + x^{3} - 24 x^{2} + 96 x - 72$	$5$	[1,2]	$3^{2}\cdot 13^{2}\cdot 557^{2}$	$3$	$54.2960105889$	$147.38724503836823$		$D_{5}$ (as 5T2)	$[121]$	$2$	$2$	$18.8582313864$
5.1.10360232000.1	$x^{5} - 2 x^{4} - 55 x^{3} - 200 x^{2} - 430 x - 640$	$5$	[1,2]	$2^{6}\cdot 5^{3}\cdot 109^{3}$	$3$	$100.710301507$	$319.03796774205216$		$F_5$ (as 5T3)	$[145]$	$2$	$2$	$102.098527304$
5.1.19172375352.1	$x^{5} - x^{4} + 25 x^{3} - 90 x^{2} - 126 x + 720$	$5$	[1,2]	$2^{3}\cdot 3^{5}\cdot 13^{3}\cdot 67^{2}$	$4$	$113.903005722$	$1187.8516612472674$	?	$S_5$ (as 5T5)	$[219]$	$2$	$2$	$104.975257029$
5.1.22415542848.4	$x^{5} - x^{4} + 7 x^{3} - 143 x^{2} + 134 x - 146$	$5$	[1,2]	$2^{6}\cdot 3^{2}\cdot 17^{3}\cdot 89^{2}$	$4$	$117.519477578$	$386.9343761898502$		$F_5$ (as 5T3)	$[170]$	$2$	$2$	$97.2714424066$
5.1.26881242025.1	$x^{5} - 2 x^{4} - 16 x^{3} - 97 x^{2} - 150 x - 76$	$5$	[1,2]	$5^{2}\cdot 11^{4}\cdot 271^{2}$	$3$	$121.868051159$	$250.65928454524635$		$D_{5}$ (as 5T2)	$[145]$	$2$	$2$	$48.3048944186$
5.1.27922744201.1	$x^{5} - x^{4} + 29 x^{3} - 52 x^{2} + 377 x - 1530$	$5$	[1,2]	$11^{4}\cdot 1381^{2}$	$2$	$122.79809218$	$253.05270696200634$	?	$A_5$ (as 5T4)	$[150]$	$2$	$2$	$159.74081387$
5.1.31266726976.1	$x^{5} - 93 x^{3} - 62 x^{2} + 2294 x + 2108$	$5$	[1,2]	$2^{6}\cdot 23^{2}\cdot 31^{4}$	$3$	$125.607763902$	$211.59152398339683$		$D_{5}$ (as 5T2)	$[5, 25]$	$2$	$2$	$152.951109318$
5.1.38613822016.1	$x^{5} - 2 x^{4} + 61 x^{3} - 108 x^{2} + 554 x - 912$	$5$	[1,2]	$2^{6}\cdot 7^{2}\cdot 11^{4}\cdot 29^{2}$	$4$	$131.023307409$	$274.41456629259625$		$D_{5}$ (as 5T2)	$[5, 25]$	$2$	$2$	$271.852313806$
5.1.47463076672.1	$x^{5} - 2 x^{4} + 72 x^{3} - 196 x^{2} - 865 x - 3222$	$5$	[1,2]	$2^{6}\cdot 11^{4}\cdot 37^{3}$	$3$	$136.543546059$	$288.94184039779174$		$F_5$ (as 5T3)	$[5, 25]$	$2$	$2$	$257.935785535$
5.1.58505450641.1	$x^{5} - 2 x^{4} + 39 x^{3} - 75 x^{2} + 37 x + 1$	$5$	[1,2]	$11^{4}\cdot 1999^{2}$	$2$	$142.376812484$	$304.4532014408089$	✓	$D_{5}$ (as 5T2)	$[2, 110]$	$2$	$2$	$13.5047098262$
5.1.82445359689.1	$x^{5} - x^{4} + 18 x^{3} - 41 x^{2} + 3 x + 505$	$5$	[1,2]	$3^{2}\cdot 7^{2}\cdot 11^{4}\cdot 113^{2}$	$4$	$152.487148568$	$331.7134011177388$	?	$A_5$ (as 5T4)	$[120]$	$2$	$2$	$56.5285673318$
5.1.121945000000.8	$x^{5} + 75 x^{3} - 30 x^{2} - 1460 x + 2568$	$5$	[1,2]	$2^{6}\cdot 5^{7}\cdot 29^{3}$	$3$	$164.904611082$	$428.29893909420633$		$F_5$ (as 5T3)	$[140]$	$2$	$2$	$344.4645634009188$
5.1.122265703125.1	$x^{5} - 30 x^{3} + 405 x - 603$	$5$	[1,2]	$3^{4}\cdot 5^{7}\cdot 139^{2}$	$3$	$164.991256501$	$783.0275526655305$	?	$S_5$ (as 5T5)	$[140]$	$2$	$2$	$47.1635175667$
5.1.172225000000.3	$x^{5} - 65 x^{3} - 90 x^{2} + 2060 x + 568$	$5$	[1,2]	$2^{6}\cdot 5^{8}\cdot 83^{2}$	$3$	$176.692956942$	$338.4044354042672$		$D_{5}$ (as 5T2)	$[20, 20]$	$2$	$2$	$109.116786659$
5.1.282245496624.1	$x^{5} - x^{4} + 34 x^{3} - 354 x^{2} - 1800 x - 2196$	$5$	[1,2]	$2^{4}\cdot 3^{4}\cdot 7^{3}\cdot 13^{3}\cdot 17^{2}$	$5$	$195.04077064$	$1532.923827815063$	?	$S_5$ (as 5T5)	$[2, 72]$	$2$	$2$	$177.468740404$
5.1.298262478125.3	$x^{5} + 10 x^{3} - 105 x^{2} - 15 x + 478$	$5$	[1,2]	$5^{5}\cdot 457^{3}$	$2$	$197.205818433$	$629.1477605017106$	✓	$F_5$ (as 5T3)	$[285]$	$2$	$2$	$53.8463547141$
5.1.350084039041.1	$x^{5} - x^{4} - 49 x^{3} - 355 x^{2} - 924 x - 1936$	$5$	[1,2]	$11^{2}\cdot 19^{4}\cdot 149^{2}$	$3$	$203.626577674$	$426.86677948262195$		$A_5$ (as 5T4)	$[120]$	$2$	$2$	$427.131001284$
5.1.366218625600.1	$x^{5} - 2 x^{4} + 18 x^{3} - 204 x^{2} + 705 x - 450$	$5$	[1,2]	$2^{6}\cdot 3^{4}\cdot 5^{2}\cdot 41^{4}$	$4$	$205.469841391$	$698.0937579019886$	?	$A_5$ (as 5T4)	$[150]$	$2$	$2$	$599.515918045$
5.1.449307000000.1	$x^{5} - 15 x^{3} - 260 x^{2} + 1635 x - 2178$	$5$	[1,2]	$2^{6}\cdot 3^{5}\cdot 5^{6}\cdot 43^{2}$	$4$	$214.04674945$	$1104.4272327161757$	?	$S_5$ (as 5T5)	$[2, 60]$	$2$	$2$	$337.483890275$
5.1.505870703125.2	$x^{5} + 10 x^{3} - 115 x^{2} - 15 x + 568$	$5$	[1,2]	$5^{8}\cdot 109^{3}$	$2$	$219.183524267$	$443.0185184609755$	✓	$F_5$ (as 5T3)	$[10, 20]$	$2$	$2$	$55.0041668144$
5.1.618582250000.1	$x^{5} + 110 x^{3} - 2420 x^{2} + 13805 x - 26356$	$5$	[1,2]	$2^{4}\cdot 5^{6}\cdot 11^{4}\cdot 13^{2}$	$4$	$228.181006145$	$397.90264455598344$		$D_{5}$ (as 5T2)	$[5, 5, 5]$	$2$	$2$	$443.265850738$
5.1.646201250000.1	$x^{5} - 5 x^{3} + 5 x - 2878$	$5$	[1,2]	$2^{4}\cdot 5^{7}\cdot 719^{2}$	$3$	$230.18316578$	$649.8272924709632$	?	$F_5$ (as 5T3)	$[220]$	$2$	$2$	$111.813795576$
5.1.658696183201.1	$x^{5} - x^{4} + 43 x^{3} + 460 x^{2} - 1679 x + 14696$	$5$	[1,2]	$7^{2}\cdot 23^{2}\cdot 71^{4}$	$3$	$231.066523048$	$384.0781640645782$	?	$A_5$ (as 5T4)	$[105]$	$2$	$2$	$459.3803221$
5.1.661951468816.1	$x^{5} - 2 x^{4} + 182 x^{3} - 614 x^{2} + 7429 x + 452$	$5$	[1,2]	$2^{4}\cdot 11^{4}\cdot 41^{4}$	$3$	$231.294459694$	$265.6875653705786$		$A_5$ (as 5T4)	$[5, 60]$	$2$	$2$	$499.737779068$
5.1.715270753125.3	$x^{5} - 123$	$5$	[1,2]	$3^{4}\cdot 5^{5}\cdot 41^{4}$	$3$	$234.905991217$	$299.0470992609422$	✓	$F_5$ (as 5T3)	$[5, 45]$	$2$	$2$	$108.078352577$
5.1.865361341504.1	$x^{5} + 1364 x - 5456$	$5$	[1,2]	$2^{6}\cdot 11^{4}\cdot 31^{4}$	$3$	$244.027908658$	$300.433596444693$	?	$A_5$ (as 5T4)	$[5, 30]$	$2$	$2$	$152.604823806$
5.1.865361341504.3	$x^{5} - 2 x^{4} + 138 x^{3} + 1036 x^{2} + 12137 x + 18998$	$5$	[1,2]	$2^{6}\cdot 11^{4}\cdot 31^{4}$	$3$	$244.027908658$	$300.433596444693$	?	$A_5$ (as 5T4)	$[5, 30]$	$2$	$2$	$319.592271711$
5.1.865361341504.4	$x^{5} - 2 x^{4} + 138 x^{3} + 1036 x^{2} - 2867 x + 32638$	$5$	[1,2]	$2^{6}\cdot 11^{4}\cdot 31^{4}$	$3$	$244.027908658$	$300.433596444693$	?	$A_5$ (as 5T4)	$[5, 30]$	$2$	$2$	$254.329599647$
5.1.1567962265489.1	$x^{5} - 2 x^{4} + 14 x^{3} - 49 x^{2} + 78 x - 253$	$5$	[1,2]	$31^{4}\cdot 1303^{2}$	$2$	$274.831888018$	$563.0689289373005$	✓	$A_5$ (as 5T4)	$[5, 45]$	$2$	$2$	$35.6308194675$
5.1.1690158870125.3	$x^{5} - x^{4} - 136 x^{3} - 1746 x^{2} - 10601 x - 25642$	$5$	[1,2]	$5^{3}\cdot 11^{4}\cdot 31^{4}$	$3$	$278.987988602$	$355.1656911252685$	?	$F_5$ (as 5T3)	$[5, 30]$	$2$	$2$	$293.06134963$
5.1.1750045889449.1	$x^{5} - x^{4} + 128 x^{3} - 217 x^{2} + 20023 x + 25574$	$5$	[1,2]	$11^{4}\cdot 13^{2}\cdot 29^{4}$	$3$	$280.937612529$	$363.08158495666237$		$A_5$ (as 5T4)	$[5, 45]$	$2$	$2$	$122.55475010714628$
5.1.2028845000000.3	$x^{5} + 35 x^{3} + 875 x - 910$	$5$	[1,2]	$2^{6}\cdot 5^{7}\cdot 7^{4}\cdot 13^{2}$	$4$	$289.36751439$	$586.1362863429553$	?	$S_5$ (as 5T5)	$[2, 80]$	$2$	$2$	$198.951707966$
5.1.2064609765625.2	$x^{5} - 165 x^{3} - 1815 x^{2} - 13640 x - 53757$	$5$	[1,2]	$5^{8}\cdot 11^{4}\cdot 19^{2}$	$3$	$290.380598109$	$389.80100593594597$		$D_{5}$ (as 5T2)	$[5, 5, 5]$	$2$	$2$	$730.027199153$
5.1.2064609765625.3	$x^{5} - 165 x^{3} - 2860 x^{2} - 8415 x - 18018$	$5$	[1,2]	$5^{8}\cdot 11^{4}\cdot 19^{2}$	$3$	$290.380598109$	$389.80100593594597$		$D_{5}$ (as 5T2)	$[5, 95]$	$2$	$2$	$308.736577197$
5.1.2530050082816.2	$x^{5} - x^{4} + 184 x^{3} - 536 x^{2} + 11542 x + 4930$	$5$	[1,2]	$2^{11}\cdot 29^{3}\cdot 37^{3}$	$3$	$302.430664463$	$2255.964474553234$	?	$S_5$ (as 5T5)	$[170]$	$2$	$2$	$433.2080549756577$
5.1.2769168200000.1	$x^{5} + 21350 x - 57828$	$5$	[1,2]	$2^{6}\cdot 5^{5}\cdot 61^{4}$	$3$	$307.942667278$	$482.6411715353459$	?	$S_5$ (as 5T5)	$[130]$	$2$	$2$	$1287.12726287$
5.1.2890571228224.3	$x^{5} - 2 x^{4} + 186 x^{3} + 1954 x^{2} + 9659 x + 53404$	$5$	[1,2]	$2^{6}\cdot 461^{4}$	$2$	$310.596627012$	$382.3893021501823$	?	$A_5$ (as 5T4)	$[210]$	$2$	$2$	$1282.12787042$
5.1.3137112050000.2	$x^{5} - 356$	$5$	[1,2]	$2^{4}\cdot 5^{5}\cdot 89^{4}$	$3$	$315.722843964$	$401.93100298917904$	?	$F_5$ (as 5T3)	$[4, 40]$	$2$	$2$	$241.259813211$
5.1.3294225000000.6	$x^{5} - 110 x^{3} - 330 x^{2} + 7535 x + 30074$	$5$	[1,2]	$2^{6}\cdot 3^{2}\cdot 5^{8}\cdot 11^{4}$	$4$	$318.823739802$	$438.09850979985436$	?	$A_5$ (as 5T4)	$[5, 30]$	$2$	$2$	$724.829728745$
5.1.4240798862400.1	$x^{5} - 2 x^{4} - 339 x^{3} + 5428 x^{2} - 28910 x + 58800$	$5$	[1,2]	$2^{6}\cdot 3^{2}\cdot 5^{2}\cdot 131^{4}$	$4$	$335.343223694$	$541.2621515427305$		$D_{5}$ (as 5T2)	$[11, 55]$	$2$	$2$	$1069.19104848$
5.1.4809797265625.1	$x^{5} + 165 x^{3} - 2530 x^{2} + 12760 x - 22176$	$5$	[1,2]	$5^{8}\cdot 11^{4}\cdot 29^{2}$	$3$	$343.894598298$	$481.5763536024488$		$A_5$ (as 5T4)	$[5, 30]$	$2$	$2$	$1351.2932920027217$
5.1.5772006250000.2	$x^{5} + 310 x^{3} - 1860 x^{2} + 7285 x + 73532$	$5$	[1,2]	$2^{4}\cdot 5^{8}\cdot 31^{4}$	$3$	$356.668995402$	$409.705088296567$		$A_5$ (as 5T4)	$[15, 30]$	$2$	$2$	$422.336363457$
5.1.6194123253125.1	$x^{5} - 211$	$5$	[1,2]	$5^{5}\cdot 211^{4}$	$2$	$361.739528829$	$460.512548973139$	✓	$F_5$ (as 5T3)	$[5, 5, 5]$	$2$	$2$	$573.828965$
5.1.7788252073536.4	$x^{5} - x^{4} - 136 x^{3} + 3028 x^{2} + 12928 x + 13232$	$5$	[1,2]	$2^{6}\cdot 3^{2}\cdot 11^{4}\cdot 31^{4}$	$4$	$378.693629963$	$520.3662533428528$	?	$A_5$ (as 5T4)	$[5, 75]$	$2$	$2$	$182.251510113$
5.1.11459816005225.1	$x^{5} - x^{4} + 498 x^{3} - 1157 x^{2} - 14097 x + 46567$	$5$	[1,2]	$5^{2}\cdot 7^{2}\cdot 311^{4}$	$3$	$409.105698559$	$583.7707535599442$	?	$A_5$ (as 5T4)	$[120]$	$2$	$2$	$705.54375276$
5.1.11567205000000.1	$x^{5} + 4875 x - 19500$	$5$	[1,2]	$2^{6}\cdot 3^{4}\cdot 5^{7}\cdot 13^{4}$	$4$	$409.869579774$	$642.3920917089204$		$S_5$ (as 5T5)	$[10, 20]$	$2$	$2$	$1632.30631838$
5.1.11956498405489.1	$x^{5} - 902 x^{2} + 5863 x - 2706$	$5$	[1,2]	$11^{4}\cdot 17^{2}\cdot 41^{4}$	$3$	$412.591999181$	$547.7289477180464$	?	$A_5$ (as 5T4)	$[5, 5, 30]$	$2$	$2$	$240.96802964699742$
5.1.12973885317184.4	$x^{5} - 2 x^{4} + 270 x^{3} + 3918 x^{2} - 381 x + 88012$	$5$	[1,2]	$2^{6}\cdot 11^{4}\cdot 61^{4}$	$3$	$419.386079415$	$516.3248287058792$	?	$A_5$ (as 5T4)	$[5, 30]$	$2$	$2$	$969.416026926$
5.1.14288951250000.2	$x^{5} + 70 x^{3} + 980 x - 1078$	$5$	[1,2]	$2^{4}\cdot 3^{2}\cdot 5^{7}\cdot 7^{4}\cdot 23^{2}$	$5$	$427.56295596$	$831.2477458971347$	?	$F_5$ (as 5T3)	$[5, 30]$	$2$	$2$	$1021.58646294$
5.1.16563556927225.3	$x^{5} - x^{4} - 477 x^{3} - 723 x^{2} + 70216 x + 105984$	$5$	[1,2]	$5^{2}\cdot 7^{2}\cdot 11^{4}\cdot 31^{4}$	$4$	$440.383177735$	$628.4019519328616$	?	$A_5$ (as 5T4)	$[5, 60]$	$2$	$2$	$2464.50509053$

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Elliptic curves over $\Q$
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