Number field search results

Results (1-50 of 160510 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
16.0.2779733938787757.1	x^16 - 5x^15 + 14x^14 - 26x^13 + 39x^12 - 53x^11 + 74x^10 - 107x^9 + 153x^8 - 196x^7 + 213x^6 - 191x^5 + 138x^4 - 77x^3 + 31x^2 - 8x + 1	$16$	[0,8]	$3^{8}\cdot 7^{2}\cdot 37^{2}\cdot 151^{2}\cdot 277$	$5$	$9.23103083876$			not computed	16T1905	trivial	$6$	$7$	$20.5837782538$
16.0.3006123291015625.1	x^16 - x^15 - 3x^14 + 6x^13 + x^12 - 10x^11 + 8x^10 + 5x^9 - 13x^8 + 5x^7 + 8x^6 - 10x^5 + x^4 + 6x^3 - 3x^2 - x + 1	$16$	[0,8]	$5^{12}\cdot 11^{4}\cdot 29^{2}$	$3$	$9.2763136443$			not computed	$(C_2^2\times D_4).C_2^3$ (as 16T547)	trivial	$10$	$7$	$35.8754367412$
16.0.3091162921500672.1	x^16 - 2x^15 + 8x^14 - 18x^13 + 35x^12 - 62x^11 + 92x^10 - 118x^9 + 138x^8 - 142x^7 + 127x^6 - 104x^5 + 77x^4 - 46x^3 + 20x^2 - 6x + 1	$16$	[0,8]	$2^{16}\cdot 3^{8}\cdot 193^{3}$	$3$	$9.29250104192$			not computed	16T1202	trivial	$12$	$7$	$43.8698041698$
16.0.3100665090835456.1	x^16 + 2x^14 + 4x^12 + 6x^10 + 8x^8 + 7x^6 + 5x^4 + 3x^2 + 1	$16$	[0,8]	$2^{10}\cdot 1740113^{2}$	$2$	$9.29428378397$			not computed	16T1945	trivial	$2$	$7$	$7.31402076949$
16.0.3143861048180736.1	x^16 - 4x^15 + 8x^14 - 8x^13 - 4x^12 + 30x^11 - 56x^10 + 58x^9 - 18x^8 - 48x^7 + 98x^6 - 102x^5 + 73x^4 - 40x^3 + 18x^2 - 6x + 1	$16$	[0,8]	$2^{24}\cdot 3^{8}\cdot 13^{4}$	$3$	$9.30232393605$			not computed	$C_2\wr C_2^2$ (as 16T149)	trivial	$12$	$7$	$44.6663869612$
16.0.3207314697265625.1	x^16 - 2x^15 - x^14 + x^13 + 11x^12 - 11x^11 - 10x^10 + 5x^9 + 22x^8 - 10x^7 - 15x^6 + 3x^5 + 11x^4 - 2x^3 - 4x^2 + x + 1	$16$	[0,8]	$5^{12}\cdot 181^{2}\cdot 401$	$3$	$9.31394884654$			not computed	16T1771	trivial	$10$	$7$	$37.3668375913$
16.0.3243658447265625.1	x^16 - 5x^15 + 14x^14 - 30x^13 + 57x^12 - 100x^11 + 157x^10 - 215x^9 + 250x^8 - 240x^7 + 183x^6 - 110x^5 + 57x^4 - 30x^3 + 16x^2 - 5x + 1	$16$	[0,8]	$3^{12}\cdot 5^{14}$	$2$	$9.3205103882$		✓	not computed	$C_8: C_2$ (as 16T6)	trivial	$30$	$7$	$112.874368042$
16.0.3345005787800625.1	x^16 - 5x^15 + 12x^14 - 19x^13 + 21x^12 - 16x^11 + 6x^10 + 12x^9 - 28x^8 + 21x^7 + x^6 - 20x^5 + 28x^4 - 20x^3 + 10x^2 - 4x + 1	$16$	[0,8]	$3^{8}\cdot 5^{4}\cdot 13^{8}$	$3$	$9.33845014563$			not computed	$D_8:C_2$ (as 16T47)	trivial	$6$	$7$	$22.9306095521$
16.0.3347302586328125.1	x^16 - 6x^15 + 20x^14 - 45x^13 + 76x^12 - 98x^11 + 94x^10 - 58x^9 + 8x^8 + 28x^7 - 37x^6 + 28x^5 - 13x^4 + 6x^2 - 4x + 1	$16$	[0,8]	$5^{8}\cdot 61^{2}\cdot 101\cdot 151^{2}$	$4$	$9.33885077346$			✓	16T1905	trivial	$2$	$7$	$7.65571718077$
16.0.3571460308796416.1	x^16 - 2x^14 + 4x^10 - 4x^8 + x^6 + 3x^4 - 3x^2 + 1	$16$	[0,8]	$2^{10}\cdot 1867553^{2}$	$2$	$9.37676138074$			not computed	16T1945	trivial	$2$	$7$	$7.9464198774$
16.0.3692461181640625.1	x^16 - 2x^15 - 2x^14 + 9x^13 - 3x^12 - 15x^11 + 17x^10 + 8x^9 - 25x^8 + 8x^7 + 17x^6 - 15x^5 - 3x^4 + 9x^3 - 2x^2 - 2x + 1	$16$	[0,8]	$5^{12}\cdot 3889^{2}$	$2$	$9.39630804632$			✓	16T1497	trivial	$10$	$7$	$40.8735633138$
16.0.3750900906670801.1	x^16 - 4x^15 + 10x^14 - 18x^13 + 29x^12 - 43x^11 + 58x^10 - 73x^9 + 85x^8 - 88x^7 + 81x^6 - 65x^5 + 45x^4 - 26x^3 + 12x^2 - 4x + 1	$16$	[0,8]	$13^{2}\cdot 43^{2}\cdot 331^{4}$	$3$	$9.40553436247$			not computed	16T1664	trivial	$2$	$7$	$8.20527213707$
16.0.3914091521024229.1	x^16 - 2x^15 + x^14 - x^13 + 4x^12 - 4x^11 + 5x^10 - 8x^9 + 6x^8 - 5x^7 + 8x^6 - 7x^5 + 7x^4 - 7x^3 + 4x^2 - 2x + 1	$16$	[0,8]	$3^{8}\cdot 61\cdot 98893^{2}$	$3$	$9.43060241959$			✓	16T1905	trivial	$6$	$7$	$25.217952399$
16.0.4045039500390625.1	x^16 - 5x^15 + 10x^14 - 6x^13 - 12x^12 + 27x^11 - 16x^10 - 14x^9 + 32x^8 - 27x^7 + 16x^6 - 11x^5 + 8x^4 - 3x^3 + 1	$16$	[0,8]	$5^{8}\cdot 11^{4}\cdot 29^{4}$	$3$	$9.45001880937$			not computed	$C_4^2:C_4.C_2$ (as 16T388)	trivial	$2$	$7$	$8.56826776068$
16.0.4096000000000000.1	x^16 - 6x^15 + 18x^14 - 36x^13 + 47x^12 - 30x^11 - 18x^10 + 72x^9 - 95x^8 + 72x^7 - 18x^6 - 30x^5 + 47x^4 - 36x^3 + 18x^2 - 6x + 1	$16$	[0,8]	$2^{24}\cdot 5^{12}$	$2$	$9.45741609003$		✓	not computed	$C_2^2 : C_4$ (as 16T10)	trivial	$20$	$7$	$87.2940978199$
16.0.4186494384765625.1	x^16 - 4x^15 + 8x^14 - 6x^13 - 5x^12 + 15x^11 - 6x^10 - 17x^9 + 26x^8 - 7x^7 - 16x^6 + 17x^5 - 2x^4 - 9x^3 + 9x^2 - 4x + 1	$16$	[0,8]	$5^{12}\cdot 41^{2}\cdot 101^{2}$	$3$	$9.47034187384$			not computed	16T1720	trivial	$10$	$7$	$43.5759224128$
16.0.4393378612917909.1	x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 6x^11 + 4x^10 - x^8 + 4x^6 + 6x^5 + 6x^4 + 6x^3 + 5x^2 + 3x + 1	$16$	[0,8]	$3^{8}\cdot 61\cdot 104773^{2}$	$3$	$9.49893496957$			not computed	16T1905	trivial	$6$	$7$	$27.0045913409$
16.0.4540317078515625.1	x^16 - 3x^15 + 4x^14 - 3x^13 + 11x^10 - 24x^9 + 29x^8 - 24x^7 + 11x^6 - 3x^3 + 4x^2 - 3x + 1	$16$	[0,8]	$3^{8}\cdot 5^{8}\cdot 11^{6}$	$3$	$9.51848624089$			not computed	$D_4:D_4$ (as 16T141)	trivial	$6$	$7$	$27.6507723749$
16.0.4559007230078125.1	x^16 - 2x^15 + 3x^14 - 6x^13 + 11x^12 - 19x^11 + 26x^10 - 30x^9 + 33x^8 - 30x^7 + 26x^6 - 19x^5 + 11x^4 - 6x^3 + 3x^2 - 2x + 1	$16$	[0,8]	$5^{8}\cdot 11^{4}\cdot 59^{2}\cdot 229$	$4$	$9.52093044767$			not computed	16T1823	trivial	$2$	$7$	$9.23010708309$
16.0.4897760256000000.1	x^16 - 4x^15 + 8x^14 - 6x^13 - 10x^12 + 28x^11 - 8x^10 - 90x^9 + 253x^8 - 396x^7 + 433x^6 - 352x^5 + 218x^4 - 102x^3 + 35x^2 - 8x + 1	$16$	[0,8]	$2^{16}\cdot 3^{14}\cdot 5^{6}$	$3$	$9.5636757927$			not computed	$(C_4\times C_8):C_2$ (as 16T114)	trivial	$12$	$7$	$59.5214550029$
16.0.4919707275390625.1	x^16 - 5x^15 + 14x^14 - 29x^13 + 50x^12 - 77x^11 + 112x^10 - 149x^9 + 176x^8 - 182x^7 + 159x^6 - 118x^5 + 73x^4 - 36x^3 + 15x^2 - 4x + 1	$16$	[0,8]	$5^{12}\cdot 67^{4}$	$2$	$9.56634862885$			not computed	$C_4\times S_4$ (as 16T181)	trivial	$10$	$7$	$48.4508350282$
16.0.5190614520439741.1	x^16 - 3x^15 + 7x^14 - 12x^13 + 15x^12 - 15x^11 + 12x^10 - 5x^9 - 2x^8 + 4x^7 - 5x^6 + 6x^5 + 3x^4 - 5x^3 - x^2 + 1	$16$	[0,8]	$617^{2}\cdot 2389^{3}$	$2$	$9.59845147343$			not computed	16T1948	trivial	$2$	$7$	$10.0160978095$
16.0.5236602731044893.1	x^16 - 7x^15 + 26x^14 - 66x^13 + 125x^12 - 180x^11 + 195x^10 - 148x^9 + 60x^8 + 21x^7 - 58x^6 + 51x^5 - 22x^4 - 2x^3 + 9x^2 - 5x + 1	$16$	[0,8]	$3^{8}\cdot 13^{4}\cdot 181^{2}\cdot 853$	$4$	$9.6037445943$			not computed	16T1823	trivial	$6$	$7$	$29.7678343854$
16.0.5415791883780096.1	x^16 - 4x^15 + 11x^14 - 24x^13 + 46x^12 - 84x^11 + 143x^10 - 208x^9 + 259x^8 - 284x^7 + 278x^6 - 234x^5 + 160x^4 - 84x^3 + 32x^2 - 8x + 1	$16$	[0,8]	$2^{16}\cdot 3^{10}\cdot 7^{2}\cdot 13^{4}$	$4$	$9.62396141075$			not computed	$(C_2\times D_4).C_2^4$ (as 16T595)	trivial	$12$	$7$	$63.1744988972$
16.0.5455162516701184.1	x^16 - 4x^13 + 3x^12 + 8x^10 - 8x^9 + x^8 - 8x^7 + 8x^6 + 3x^4 - 4x^3 + 1	$16$	[0,8]	$2^{32}\cdot 7^{4}\cdot 23^{2}$	$3$	$9.628319226$			not computed	$C_2\times C_4^2:C_4.C_2$ (as 16T509)	trivial	$8$	$7$	$40.8921494432$
16.0.5572562780160000.1	x^16 - 2x^14 - 7x^12 + 4x^10 + 34x^8 + 50x^6 + 32x^4 + 8x^2 + 1	$16$	[0,8]	$2^{24}\cdot 3^{12}\cdot 5^{4}$	$3$	$9.64114102734$			not computed	$C_2^2:D_4$ (as 16T43)	trivial	$12$	$7$	$62.6647388247$
16.0.5575888916015625.1	x^16 - 5x^15 + 15x^14 - 30x^13 + 49x^12 - 70x^11 + 90x^10 - 105x^9 + 111x^8 - 105x^7 + 90x^6 - 70x^5 + 49x^4 - 30x^3 + 15x^2 - 5x + 1	$16$	[0,8]	$3^{8}\cdot 5^{12}\cdot 59^{2}$	$3$	$9.64150058785$			not computed	$C_2\times C_2\wr C_4$ (as 16T261)	trivial	$30$	$7$	$155.628338249$
16.0.5605632412826517.1	x^16 - 4x^15 + 11x^14 - 24x^13 + 46x^12 - 75x^11 + 104x^10 - 121x^9 + 121x^8 - 107x^7 + 86x^6 - 63x^5 + 43x^4 - 27x^3 + 14x^2 - 5x + 1	$16$	[0,8]	$3^{10}\cdot 37^{7}$	$2$	$9.64470699747$			not computed	$C_2^2:\OD_{16}.C_2^2$ (as 16T675)	trivial	$6$	$7$	$32.1900879299$
16.0.5821863490955437.1	x^16 - 4x^15 + 10x^14 - 17x^13 + 23x^12 - 27x^11 + 30x^10 - 30x^9 + 25x^8 - 14x^7 + 6x^6 - 7x^5 + 15x^4 - 20x^3 + 15x^2 - 6x + 1	$16$	[0,8]	$19^{2}\cdot 101^{2}\cdot 277\cdot 2389^{2}$	$4$	$9.66754886986$			not computed	16T1948	trivial	$2$	$7$	$10.6211653408$
16.0.5850424087444225.1	x^16 - x^15 - 2x^14 + 6x^13 + x^12 - 16x^11 + 16x^10 + 5x^9 - 19x^8 + 5x^7 + 16x^6 - 16x^5 + x^4 + 6x^3 - 2x^2 - x + 1	$16$	[0,8]	$5^{2}\cdot 37^{2}\cdot 643^{4}$	$3$	$9.67050623513$			not computed	16T1664	trivial	$2$	$7$	$10.6388599051$
16.0.5960322509765625.1	x^16 - 5x^15 + 11x^14 - 10x^13 - 10x^12 + 45x^11 - 56x^10 - 10x^9 + 159x^8 - 315x^7 + 374x^6 - 300x^5 + 160x^4 - 50x^3 + 6x^2 + 1	$16$	[0,8]	$3^{8}\cdot 5^{12}\cdot 61^{2}$	$3$	$9.68176105277$			not computed	$C_2\times C_2\wr C_4$ (as 16T261)	trivial	$30$	$7$	$161.821613678$
16.0.6158959248447369.1	x^16 - 3x^15 + 2x^14 + 6x^13 - 10x^12 - 3x^11 + 23x^10 - 24x^9 + 7x^8 + 6x^7 + x^6 - 15x^5 + 20x^4 - 15x^3 + 7x^2 - 3x + 1	$16$	[0,8]	$3^{12}\cdot 7^{4}\cdot 13^{6}$	$3$	$9.70161884492$			not computed	$C_2.(C_2^3.D_4)$ (as 16T211)	trivial	$6$	$7$	$33.7844971841$
16.0.6158959248447369.2	x^16 - 3x^15 + 7x^14 - 12x^13 + 17x^12 - 18x^11 + 13x^10 + 3x^9 - 29x^8 + 45x^7 - 34x^6 + 3x^5 + 23x^4 - 27x^3 + 17x^2 - 6x + 1	$16$	[0,8]	$3^{12}\cdot 7^{4}\cdot 13^{6}$	$3$	$9.70161884492$			not computed	$C_2.(C_2^3.D_4)$ (as 16T211)	trivial	$6$	$7$	$33.0234170129$
16.0.6298009600000000.1	x^16 - 4x^15 + 8x^14 - 10x^13 + 11x^12 - 12x^11 + 10x^10 - 4x^9 + x^8 - 4x^7 + 10x^6 - 12x^5 + 11x^4 - 10x^3 + 8x^2 - 4x + 1	$16$	[0,8]	$2^{24}\cdot 5^{8}\cdot 31^{2}$	$3$	$9.71516559153$			not computed	$C_4^2:C_4.C_2$ (as 16T396)	trivial	$4$	$7$	$22.3523537457$
16.0.6468474822995241.1	x^16 - 4x^15 + 9x^14 - 14x^13 + 16x^12 - 9x^11 - 8x^10 + 27x^9 - 35x^8 + 27x^7 - 8x^6 - 9x^5 + 16x^4 - 14x^3 + 9x^2 - 4x + 1	$16$	[0,8]	$3^{2}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$	$4$	$9.73139538561$			✓	16T1664	trivial	$2$	$7$	$11.6239832087$
16.0.6472705322265625.1	x^16 - x^15 + x^14 + x^13 + 3x^12 + 4x^11 + 4x^10 + 8x^9 + 8x^8 + 9x^7 + 6x^6 + 8x^5 + 8x^4 + 3x^3 + 4x^2 + 3x + 1	$16$	[0,8]	$5^{12}\cdot 19^{2}\cdot 271^{2}$	$3$	$9.73179304548$			not computed	16T1497	trivial	$10$	$7$	$56.3298547938$
16.0.6561000000000000.1	x^16 - 5x^15 + 15x^14 - 32x^13 + 56x^12 - 85x^11 + 114x^10 - 134x^9 + 131x^8 - 98x^7 + 42x^6 + 9x^5 - 28x^4 + 18x^3 - x^2 - 3x + 1	$16$	[0,8]	$2^{12}\cdot 3^{8}\cdot 5^{12}$	$3$	$9.74003746425$			not computed	$C_4 \times D_4$ (as 16T19)	trivial	$30$	$7$	$175.01473438$
16.0.6634204312890625.1	x^16 - 7x^15 + 27x^14 - 73x^13 + 160x^12 - 304x^11 + 509x^10 - 730x^9 + 869x^8 - 839x^7 + 654x^6 - 416x^5 + 221x^4 - 98x^3 + 34x^2 - 8x + 1	$16$	[0,8]	$5^{8}\cdot 19^{8}$	$2$	$9.74679434481$		✓	not computed	$D_{8}$ (as 16T13)	trivial	$2$	$7$	$11.4915268613$
16.0.6741949462890625.1	x^16 + x^14 - 5x^13 + 2x^12 - 5x^11 + 13x^10 - 10x^9 + 15x^8 - 20x^7 + 17x^6 - 20x^5 + 17x^4 - 10x^3 + 9x^2 - 5x + 1	$16$	[0,8]	$5^{14}\cdot 1051^{2}$	$2$	$9.75661332423$			not computed	16T1497	trivial	$10$	$7$	$58.1502195758$
16.0.6788091008176384.1	x^16 - 2x^14 - 4x^12 + 10x^10 + 3x^8 - 12x^6 - x^4 + 5x^2 + 1	$16$	[0,8]	$2^{8}\cdot 47^{2}\cdot 331^{4}$	$3$	$9.76077335363$			not computed	16T1852	trivial	$2$	$7$	$11.7319712743$
16.0.6884340550074368.1	x^16 - 6x^15 + 22x^14 - 56x^13 + 110x^12 - 174x^11 + 232x^10 - 266x^9 + 259x^8 - 202x^7 + 112x^6 - 30x^5 - 14x^4 + 20x^3 - 6x^2 - 2x + 1	$16$	[0,8]	$2^{24}\cdot 17^{7}$	$2$	$9.7693663658$			not computed	$C_8^2.C_2$ (as 16T289)	trivial	$4$	$7$	$23.5886655901$
16.0.6926910400390625.1	x^16 - 7x^15 + 25x^14 - 55x^13 + 75x^12 - 46x^11 - 43x^10 + 140x^9 - 160x^8 + 80x^7 + 37x^6 - 109x^5 + 110x^4 - 70x^3 + 30x^2 - 8x + 1	$16$	[0,8]	$5^{15}\cdot 61^{3}$	$2$	$9.77313106739$			not computed	16T1192	trivial	$10$	$7$	$65.2827160145$
16.0.7058653305387264.1	x^16 - 2x^15 + 2x^14 - 3x^13 + 11x^12 - 19x^11 + 10x^10 + 21x^9 - 44x^8 + 21x^7 + 40x^6 - 89x^5 + 92x^4 - 60x^3 + 26x^2 - 7x + 1	$16$	[0,8]	$2^{8}\cdot 3^{14}\cdot 7^{8}$	$3$	$9.78464595129$			not computed	$D_8:C_2$ (as 16T47)	trivial	$6$	$7$	$37.0149239843$
16.0.7105708251953125.1	x^16 - 2x^15 + 4x^14 - 5x^13 + 3x^12 + 5x^11 - 14x^10 + 17x^9 - 12x^8 - 3x^7 + 31x^6 - 60x^5 + 68x^4 - 50x^3 + 24x^2 - 7x + 1	$16$	[0,8]	$5^{12}\cdot 181\cdot 401^{2}$	$3$	$9.78870996517$			not computed	16T1771	trivial	$10$	$7$	$60.6835925321$
16.0.7213895789838336.1	x^16 - 8x^15 + 36x^14 - 108x^13 + 244x^12 - 436x^11 + 636x^10 - 780x^9 + 831x^8 - 780x^7 + 636x^6 - 436x^5 + 244x^4 - 108x^3 + 36x^2 - 8x + 1	$16$	[0,8]	$2^{40}\cdot 3^{8}$	$2$	$9.79795897113$		✓	not computed	$Q_8 : C_2$ (as 16T11)	trivial	$24$	$7$	$168.461389974$
16.0.7380528100000000.1	x^16 + 2x^14 + 2x^12 + 4x^6 + 5x^4 + 4x^2 + 1	$16$	[0,8]	$2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 71^{2}$	$4$	$9.81195312751$			not computed	16T1728	trivial	$2$	$7$	$12.3463543204$
16.0.7771775074107392.1	x^16 - 6x^15 + 17x^14 - 28x^13 + 26x^12 - 10x^11 - 3x^10 + 2x^9 + x^8 + 6x^7 - 10x^6 + 2x^5 + 6x^4 - 4x^3 - 2x^2 + 2x + 1	$16$	[0,8]	$2^{16}\cdot 17^{9}$	$2$	$9.84368060738$			not computed	$C_8.\SD_{16}$ (as 16T260)	trivial	$4$	$7$	$25.2889722607$
16.0.8067379209183488.1	x^16 - 3x^15 + 3x^14 + x^13 + x^12 - 18x^11 + 36x^10 - 33x^9 + 23x^8 - 42x^7 + 92x^6 - 129x^5 + 120x^4 - 76x^3 + 32x^2 - 8x + 1	$16$	[0,8]	$2^{8}\cdot 17^{3}\cdot 283^{4}$	$3$	$9.86667400786$			not computed	16T1851	trivial	$2$	$7$	$13.0020519042$
16.0.8084777718513664.1	x^16 - 4x^15 + 6x^14 - 14x^12 + 24x^11 - 18x^10 + 15x^8 - 20x^7 + 22x^6 - 24x^5 + 24x^4 - 20x^3 + 12x^2 - 4x + 1	$16$	[0,8]	$2^{36}\cdot 7^{6}$	$2$	$9.8680026001$			not computed	$D_4:D_4$ (as 16T141)	trivial	$8$	$7$	$60.0447869363$
16.0.8148125331379089.1	x^16 - x^15 - 6x^14 + 4x^13 + 15x^12 - 6x^11 - 20x^10 + 7x^9 + 21x^8 - 7x^7 - 20x^6 + 6x^5 + 15x^4 - 4x^3 - 6x^2 + x + 1	$16$	[0,8]	$3^{12}\cdot 7^{6}\cdot 19^{4}$	$3$	$9.87281743569$			not computed	$C_4^2:C_4.C_2$ (as 16T388)	trivial	$6$	$7$	$41.5444168882$