Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 15950 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator	Unit signature rank	Max $p$
7.1.211831.1	$x^{7} - x^{6} + 2 x^{5} - x^{4} + x^{2} - 2 x + 1$	$7$	(1, 3)	$-\,19\cdot 11149$	$2$	$5.76574784303$	$460.2510184670969$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$0.418943361216$	$1$	$11149$
7.1.549727.1	$x^{7} - x^{6} + x^{5} - 2 x^{4} + x^{3} - 3 x^{2} + x - 1$	$7$	(1, 3)	$-\,19\cdot 28933$	$2$	$6.60725410917$	$741.4357693016975$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$0.934617998246$	$1$	$28933$
7.1.765263.1	$x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{4} + 6 x^{3} - 5 x^{2} + 3 x - 1$	$7$	(1, 3)	$-\,19\cdot 40277$	$2$	$6.92698724572$	$874.7931184000021$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1.0799284022$	$1$	$40277$
7.3.765529.1	$x^{7} - 2 x^{6} + 3 x^{4} - 4 x^{3} + 2 x - 1$	$7$	(3, 2)	$19\cdot 43\cdot 937$	$3$	$6.92733116187$	$874.9451411374315$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1.1694260469$	$3$	$937$
7.1.797012.1	$x^{7} - x^{6} + 2 x^{5} + x^{3} + 2 x - 1$	$7$	(1, 3)	$-\,2^{2}\cdot 19\cdot 10487$	$3$	$6.96733044447$	$892.755285618629$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1.50319820387$	$1$	$10487$
7.3.1078193.1	$x^{7} - x^{6} + 2 x^{4} - 3 x^{3} + x - 1$	$7$	(3, 2)	$19\cdot 56747$	$2$	$7.27467820089$	$1038.3607273004889$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1.47057938819$	$3$	$56747$
7.1.1253696.1	$x^{7} - x^{6} - 2 x^{4} + x^{3} + x^{2} + x + 1$	$7$	(1, 3)	$-\,2^{6}\cdot 19\cdot 1031$	$3$	$7.43310589588$	$470.76983313144916$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.04887843117$	$1$	$1031$
7.3.1282481.1	$x^{7} - 3 x^{6} + 6 x^{5} - 7 x^{4} + 4 x^{3} - x^{2} - 2 x + 1$	$7$	(3, 2)	$19\cdot 67499$	$2$	$7.4572500493$	$1132.4667765546149$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1.7229807626$	$3$	$67499$
7.1.1576259.1	$x^{7} - x^{6} + 2 x^{5} - x^{3} + 4 x^{2} - 2 x + 1$	$7$	(1, 3)	$-\,19\cdot 23\cdot 3607$	$3$	$7.68025020299$	$1255.4915372076389$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1.74719545002$	$1$	$3607$
7.1.1736239.1	$x^{7} - x^{6} - 3 x^{4} + 2 x^{3} + x^{2} + 2 x - 1$	$7$	(1, 3)	$-\,19\cdot 91381$	$2$	$7.78704683491$	$1317.6642212642794$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1.92691089976$	$1$	$91381$
7.1.1856851.2	$x^{7} - 2 x^{4} + x^{3} - x + 2$	$7$	(1, 3)	$-\,19\cdot 97729$	$2$	$7.8621183927$	$1362.6632012349933$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.67709961139$	$1$	$97729$
7.3.1924073.1	$x^{7} - 3 x^{6} + 2 x^{5} + 2 x^{4} - 5 x^{3} + 4 x^{2} - x + 1$	$7$	(3, 2)	$19\cdot 101267$	$2$	$7.90216211385$	$1387.109584712037$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$2.20373034584$	$3$	$101267$
7.1.2009212.1	$x^{7} - x^{6} + x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 1$	$7$	(1, 3)	$-\,2^{2}\cdot 19\cdot 26437$	$3$	$7.95119220631$	$1125.0441085800542$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.92258428162$	$1$	$26437$
7.1.2123516.1	$x^{7} + 2 x^{3} - x^{2} + x + 1$	$7$	(1, 3)	$-\,2^{2}\cdot 19\cdot 27941$	$3$	$8.01429043026$	$1156.6033261642822$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.7927473669$	$1$	$27941$
7.1.2178559.1	$x^{7} - x^{6} + x^{5} + x^{4} - 2 x^{3} + 4 x^{2} - 2 x + 1$	$7$	(1, 3)	$-\,19\cdot 114661$	$2$	$8.0436425138$	$1475.9942411811776$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.29748420498$	$1$	$114661$
7.3.2338121.1	$x^{7} - 2 x^{6} - x^{5} + 6 x^{4} - 3 x^{3} - 2 x^{2} + 3 x - 1$	$7$	(3, 2)	$19\cdot 123059$	$2$	$8.12527634268$	$1529.091560371713$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$2.4921723084$	$3$	$123059$
7.1.2339907.1	$x^{7} + 3 x^{5} - x^{4} + 2 x^{3} - x^{2} - x + 1$	$7$	(1, 3)	$-\,3\cdot 19\cdot 41051$	$3$	$8.12616270736$	$1529.6754557748516$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.62016404063$	$1$	$41051$
7.1.2437396.1	$x^{7} - x^{6} + x^{5} + 3 x^{3} + x - 1$	$7$	(1, 3)	$-\,2^{2}\cdot 13\cdot 19\cdot 2467$	$4$	$8.17368719668$	$1561.2161925883295$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.03598670598$	$1$	$2467$
7.1.2451836.1	$x^{7} - 3 x^{6} + 5 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$	$7$	(1, 3)	$-\,2^{2}\cdot 19\cdot 32261$	$3$	$8.18058738637$	$1242.8032401168832$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.27171687311$	$1$	$32261$
7.1.2599751.1	$x^{7} - 3 x^{6} + 6 x^{5} - 6 x^{4} + 7 x^{3} - 4 x^{2} + 3 x - 1$	$7$	(1, 3)	$-\,7\cdot 11\cdot 19\cdot 1777$	$4$	$8.24933275137$	$1612.3743361887152$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.53460905948$	$1$	$1777$
7.1.2707291.1	$x^{7} - x^{6} + 3 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$	$7$	(1, 3)	$-\,19\cdot 89\cdot 1601$	$3$	$8.29723828866$	$1645.384757435172$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.52071844743$	$1$	$1601$
7.3.2709153.1	$x^{7} - x^{6} + 2 x^{4} - 3 x^{3} + 3 x + 1$	$7$	(3, 2)	$3^{3}\cdot 19\cdot 5281$	$3$	$8.29805327867$	$1141.2383259931623$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$3.25269414046$	$3$	$5281$
7.1.2712079.1	$x^{7} - 3 x^{6} + 2 x^{5} + 4 x^{4} - 6 x^{3} + 2 x^{2} + 1$	$7$	(1, 3)	$-\,19\cdot 349\cdot 409$	$3$	$8.29933300773$	$1646.8390935364632$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.24864291361$	$1$	$409$
7.3.2733321.1	$x^{7} - x^{6} - x^{5} + 3 x^{4} - 3 x^{3} - 3 x^{2} + 4 x - 1$	$7$	(3, 2)	$3\cdot 19\cdot 79\cdot 607$	$4$	$8.30858819074$	$1653.2758390540885$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$3.19201219277$	$3$	$607$
7.1.2738451.1	$x^{7} - 2 x^{6} - 2 x^{5} + 5 x^{4} - x^{3} - 4 x^{2} + 3 x - 1$	$7$	(1, 3)	$-\,3\cdot 19\cdot 107\cdot 449$	$4$	$8.31081409693$	$1654.8265770164558$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.58900914705$	$1$	$449$
7.1.2884295.1	$x^{7} - 3 x^{6} + 3 x^{5} - 3 x^{4} + 4 x^{3} - x^{2} - x - 1$	$7$	(1, 3)	$-\,5\cdot 19\cdot 97\cdot 313$	$4$	$8.3726475736$	$1698.3212299208888$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.95605981789$	$1$	$313$
7.3.3077696.1	$x^{7} - x^{6} + x^{5} - x^{4} - x^{3} - 3 x^{2} - x + 1$	$7$	(3, 2)	$2^{6}\cdot 19\cdot 2531$	$3$	$8.45063586649$	$397.2359849512695$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$4.3606093371$	$3$	$2531$
7.1.3099071.1	$x^{7} - x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - x - 1$	$7$	(1, 3)	$-\,19\cdot 163109$	$2$	$8.45899541265$	$1760.4178481258364$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.68456280619$	$1$	$163109$
7.1.3169979.1	$x^{7} - x^{5} + 3 x^{3} - 2 x^{2} + 2 x + 1$	$7$	(1, 3)	$-\,19\cdot 166841$	$2$	$8.48637738538$	$1780.4434840791773$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$4.45587755406$	$1$	$166841$
7.1.3215408.1	$x^{7} - x^{6} + 3 x^{4} - x^{2} + 3 x + 2$	$7$	(1, 3)	$-\,2^{4}\cdot 7\cdot 19\cdot 1511$	$4$	$8.50364566448$	$711.6143814595422$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$4.17405274506$	$1$	$1511$
7.1.3230000.1	$x^{7} - 3 x^{6} + 8 x^{5} - 11 x^{4} + 11 x^{3} - 5 x^{2} + 1$	$7$	(1, 3)	$-\,2^{4}\cdot 5^{4}\cdot 17\cdot 19$	$4$	$8.50914794499$	$117.97308208911882$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.94135097785$	$1$	$19$
7.1.3402615.1	$x^{7} - 2 x^{6} + x^{5} + x^{4} + x^{3} - 3 x^{2} + x - 1$	$7$	(1, 3)	$-\,3\cdot 5\cdot 19\cdot 11939$	$4$	$8.57267019536$	$1844.6178466012952$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.33353567514$	$1$	$11939$
7.3.3408676.1	$x^{7} - x^{6} - x^{5} + x^{4} - x^{3} - 2 x^{2} + 2 x + 2$	$7$	(3, 2)	$2^{2}\cdot 19\cdot 44851$	$3$	$8.57485000338$	$1465.3775357687616$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$4.66373779507$	$3$	$44851$
7.3.3505025.1	$x^{7} - 2 x^{6} + 2 x^{4} - 4 x^{3} + 4 x^{2} - x + 1$	$7$	(3, 2)	$5^{2}\cdot 19\cdot 47\cdot 157$	$4$	$8.60906276889$	$1094.8523592247943$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$3.97973339061$	$3$	$157$
7.1.3509167.1	$x^{7} - x^{6} + x^{5} + 3 x^{4} - 4 x^{3} + 5 x^{2} - 3 x + 1$	$7$	(1, 3)	$-\,19\cdot 184693$	$2$	$8.61051540543$	$1873.277075074587$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2.91572762142$	$1$	$184693$
7.3.3638557.1	$x^{7} - x^{6} - 2 x^{5} - 3 x^{4} + 2 x^{3} + 3 x^{2} + 3 x + 1$	$7$	(3, 2)	$13\cdot 19\cdot 14731$	$3$	$8.65516990185$	$1907.5001965923882$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$3.73843463355$	$3$	$14731$
7.1.3779043.1	$x^{7} - 3 x^{6} + 4 x^{5} - 2 x^{4} - 3 x^{3} + 3 x^{2} - x - 2$	$7$	(1, 3)	$-\,3\cdot 19\cdot 167\cdot 397$	$4$	$8.70213820234$	$1943.9760800997526$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$5.23561607786$	$1$	$397$
7.3.3925457.1	$x^{7} - 2 x^{6} + 4 x^{5} - 8 x^{4} + 8 x^{3} - 8 x^{2} + 5 x - 1$	$7$	(3, 2)	$19\cdot 206603$	$2$	$8.74952180426$	$1981.2766086541274$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$3.33794782837$	$3$	$206603$
7.1.4047836.1	$x^{7} - 3 x^{6} + 7 x^{5} - 9 x^{4} + 7 x^{3} - 2 x^{2} - 2 x + 2$	$7$	(1, 3)	$-\,2^{2}\cdot 13\cdot 17\cdot 19\cdot 241$	$5$	$8.78797852421$	$1596.8647066865533$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$4.40235029022$	$1$	$241$
7.1.4068907.1	$x^{7} - x^{6} - x^{4} + x^{3} - 2 x^{2} - x - 1$	$7$	(1, 3)	$-\,19\cdot 23\cdot 9311$	$3$	$8.79449910592$	$2017.1531920010439$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$5.48541223861$	$1$	$9311$
7.1.4208576.1	$x^{7} - x^{6} + x^{5} - x^{4} + x^{3} - 3 x^{2} - x - 1$	$7$	(1, 3)	$-\,2^{6}\cdot 19\cdot 3461$	$3$	$8.83700345705$	$575.6775080547683$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$6.87704840688$	$1$	$3461$
7.1.4322899.1	$x^{7} + 3 x^{5} - x^{4} + 2 x^{3} - 2 x^{2} - x + 1$	$7$	(1, 3)	$-\,7\cdot 19\cdot 32503$	$3$	$8.87090380492$	$2079.1582431359093$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$4.20444622342$	$1$	$32503$
7.3.4456013.1	$x^{7} - 3 x^{6} + 2 x^{5} - x^{4} + x^{3} + 4 x^{2} - 4 x + 1$	$7$	(3, 2)	$19\cdot 234527$	$2$	$8.9094212349$	$2110.927047531487$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$3.54131293699$	$3$	$234527$
7.1.4598855.1	$x^{7} - 2 x^{6} - 2 x^{4} + 6 x^{3} - 2 x^{2} + x - 1$	$7$	(1, 3)	$-\,5\cdot 19\cdot 48409$	$3$	$8.94967165792$	$2144.494112838737$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3.67601630002$	$1$	$48409$
7.1.4674323.1	$x^{7} - x^{6} + 2 x^{5} + x^{4} + x^{3} + 3 x^{2} + 3 x + 1$	$7$	(1, 3)	$-\,19\cdot 246017$	$2$	$8.97050638987$	$2162.0182700430632$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$4.04734386034$	$1$	$246017$
7.1.4768487.1	$x^{7} - 2 x^{6} - 2 x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x - 1$	$7$	(1, 3)	$-\,19\cdot 113\cdot 2221$	$3$	$8.99610201919$	$2183.686561757433$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$5.14414673777$	$1$	$2221$
7.3.4834721.1	$x^{7} - 3 x^{5} - 2 x^{4} + 3 x^{3} + 2 x^{2} - 3 x + 1$	$7$	(3, 2)	$19\cdot 79\cdot 3221$	$3$	$9.01384742142$	$2198.7998999454226$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$4.736455134$	$3$	$3221$
7.1.4866584.1	$x^{7} - 2 x^{6} + 3 x^{5} - x^{4} - 3 x^{3} + 7 x^{2} - 6 x + 2$	$7$	(1, 3)	$-\,2^{3}\cdot 19\cdot 101\cdot 317$	$4$	$9.0223100253$	$2206.0335446225654$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$4.65693184976$	$1$	$317$
7.1.4896832.1	$x^{7} - x^{6} + 3 x^{5} - 3 x^{4} + 2 x^{3} + 2 x^{2} + x - 1$	$7$	(1, 3)	$-\,2^{6}\cdot 19\cdot 4027$	$3$	$9.03029986725$	$930.4008697238094$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$5.09786696286$	$1$	$4027$
7.3.4960577.1	$x^{7} - x^{6} - x^{5} - 2 x^{3} + 3 x^{2} + 1$	$7$	(3, 2)	$19\cdot 131\cdot 1993$	$3$	$9.04700018776$	$2227.2352816889374$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$3.96840224992$	$3$	$1993$

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