Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 750)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.21235828992734375.1	x^14 - 2x^13 - 5x^12 + 12x^11 - 10x^10 - 7x^9 + 55x^8 - 28x^7 + 65x^6 - 2x^5 + 106x^4 - 70x^3 + 50x^2 + 25x + 25	\( -\,5^{7}\cdot 43^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.82184209159918343.1	x^14 - x^13 + 7x^12 - 8x^11 + 23x^10 - 25x^9 + 47x^8 - 36x^7 + 61x^6 - 21x^5 + 78x^4 + 20x^3 + 62x^2 + 8x + 27	\( -\,17^{6}\cdot 23^{7} \)	$D_{14}$ (as 14T3)	$[3]$
14.0.160388518974780383.1	x^14 - 6x^13 + 25x^12 - 68x^11 + 149x^10 - 219x^9 + 279x^8 - 193x^7 + 254x^6 + 10x^5 + 158x^4 + 341x^3 + 334x^2 + 135x + 25	\( -\,7^{7}\cdot 41^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.370903242964296875.1	x^14 - 7x^13 + 28x^12 - 70x^11 + 119x^10 - 140x^9 + 105x^8 - 53x^7 + 14x^6 - 7x^5 + 42x^4 - 42x^3 + 35x^2 - 14x + 4	\( -\,5^{7}\cdot 7^{15} \)	$F_7$ (as 14T4)	$[2]$
14.0.371923669440000000.1	x^14 - 3x^12 - 3x^10 + 13x^8 + 51x^6 + 111x^4 + 91x^2 + 15	\( -\,2^{12}\cdot 3^{19}\cdot 5^{7} \)	$F_7$ (as 14T4)	$[2]$
14.0.710556262374296875.1	x^14 - 4x^13 + 20x^12 - 52x^11 + 151x^10 - 284x^9 + 582x^8 - 776x^7 + 1257x^6 - 1312x^5 + 2111x^4 - 2209x^3 + 2979x^2 - 2242x + 1589	\( -\,5^{7}\cdot 71^{7} \)	$D_{14}$ (as 14T3)	$[4]$
14.0.1397131555718611831.1	x^14 - 2x^13 - 7x^12 + 15x^11 + 28x^10 - 76x^9 - 28x^8 + 78x^7 - 136x^6 + 188x^5 + 421x^4 + 342x^3 + 995x^2 + 391x + 391	\( -\,17^{7}\cdot 23^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.1475921147386413091.1	x^14 - 4x^13 + 9x^12 - 20x^11 + 64x^10 - 163x^9 + 248x^8 - 197x^7 + 73x^6 - 76x^5 + 182x^4 - 203x^3 + 113x^2 - 30x + 4	\( -\,7^{7}\cdot 13^{11} \)	$F_7$ (as 14T4)	$[2]$
14.0.1756586560892125184.1	x^14 - 4x^13 + 10x^12 - 14x^11 + 54x^10 - 66x^9 + 68x^8 + 134x^7 + 369x^6 - 90x^5 + 194x^4 - 56x^3 + 264x^2 + 96x + 64	\( -\,2^{14}\cdot 101^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.2762745569510280911.1	x^14 + 6x^12 + 65x^10 + 50x^8 + 430x^6 + 575x^4 + 895x^2 + 431	\( -\,431^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.3565764541089561663.1	x^14 - 4x^13 + 4x^12 - 5x^11 + 26x^10 - 14x^9 + 55x^8 - 379x^7 + 1252x^6 - 2247x^5 + 2859x^4 - 2493x^3 + 1674x^2 - 729x + 729	\( -\,3^{7}\cdot 149^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.2.4156382630830772224.1	x^14 - x^13 - 7x^12 + 9x^11 + 25x^10 + 3x^9 - 117x^8 - 73x^7 + 406x^6 + 26x^5 - 480x^4 - 164x^3 + 456x^2 + 204x - 116	\( 2^{12}\cdot 317^{6} \)	$\PSL(2,7)$ (as 14T10)	$[3]$
14.2.4156382630830772224.2	x^14 - x^13 + x^12 + 7x^11 + 9x^10 - 5x^9 + 21x^8 + 63x^7 + 32x^6 + 74x^5 + 188x^4 + 70x^3 - 230x^2 - 144x - 22	\( 2^{12}\cdot 317^{6} \)	$\PSL(2,7)$ (as 14T10)	$[3]$
14.2.5787172169290083953.1	x^14 - 6x^13 + 20x^12 - 51x^11 + 106x^10 - 190x^9 + 304x^8 - 447x^7 + 608x^6 - 760x^5 + 848x^4 - 816x^3 + 640x^2 - 384x + 128	\( 17^{3}\cdot 23^{4}\cdot 64879^{2} \)	14T57	$[2]$
14.0.8146590668153303687.1	x^14 - 4x^13 - 2x^12 + 21x^11 + 22x^10 - 101x^9 + 29x^8 - 40x^7 + 73x^6 - 222x^5 - 475x^4 + 867x^3 + 2445x^2 + 2446x + 1403	\( -\,503^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.9098007718612700671.1	x^14 - 6x^12 + 59x^10 - 284x^8 + 1027x^6 - 1306x^4 + 2445x^2 + 511	\( -\,7^{7}\cdot 73^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.2.9524221049139396608.1	x^14 - 6x^13 + 9x^12 + 10x^11 - 35x^10 + 34x^9 - 39x^8 + 12x^7 + 15x^6 + 54x^5 + 47x^4 + 26x^3 + 3x^2 - 2x - 1	\( 2^{15}\cdot 4129^{4} \)	14T51	$[2]$
14.6.10260628712958602189.1	x^14 - 7x^13 + 30x^12 - 89x^11 + 184x^10 - 271x^9 + 254x^8 - 83x^7 - 96x^6 + 119x^5 - 37x^4 - 17x^3 + 13x^2 - x - 1	\( 29^{13} \)	$C_2\times F_8$ (as 14T9)	$[2]$
14.0.12272026890292239799.1	x^14 - 4x^13 + 26x^12 - 79x^11 + 272x^10 - 631x^9 + 1437x^8 - 2482x^7 + 3850x^6 - 4473x^5 + 4302x^4 - 2694x^3 + 1149x^2 - 54x + 109	\( -\,107^{3}\cdot 21557^{3} \)	14T54	$[2]$
14.0.12545167784987734375.1	x^14 + 6x^12 - 85x^10 + 355x^8 - 695x^6 + 1091x^4 - 609x^2 + 535	\( -\,5^{7}\cdot 107^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.12710233464526340096.1	x^14 - 2x^13 + 3x^12 - 32x^11 + 95x^10 - 138x^9 + 293x^8 - 932x^7 + 1612x^6 - 776x^5 + 868x^4 - 2384x^3 + 1840x^2 - 640x + 256	\( -\,2^{21}\cdot 67^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.19912716231399964672.1	x^14 + 28x^10 - 14x^9 + 56x^8 + 52x^7 + 98x^6 + 112x^5 + 84x^4 + 112x^3 + 56x^2 + 28x + 18	\( -\,2^{22}\cdot 7^{15} \)	14T40	$[2]$
14.0.26713070983635746816.1	x^14 + 8x^12 + 66x^10 + 212x^8 + 673x^6 + 2684x^4 + 4804x^2 + 2384	\( -\,2^{14}\cdot 149^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.28745771808565755904.1	x^14 + 16x^12 + 94x^10 + 256x^8 + 337x^6 + 204x^4 + 52x^2 + 4	\( -\,2^{26}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	$[2]$
14.0.28745771808565755904.2	x^14 + 17x^12 + 108x^10 + 328x^8 + 492x^6 + 328x^4 + 68x^2 + 4	\( -\,2^{26}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	$[2]$
14.2.28745771808565755904.1	x^14 - 5x^13 + 12x^12 - 19x^11 + 30x^10 - 23x^9 - 83x^8 + 304x^7 - 470x^6 + 402x^5 - 152x^4 - 26x^3 + 50x - 22	\( 2^{26}\cdot 809^{4} \)	14T50	$[2]$
14.2.45205467781286334025.2	x^14 - 5x^13 + 11x^12 - 22x^11 + 39x^10 - 75x^9 + 115x^8 - 179x^7 + 230x^6 - 300x^5 + 312x^4 - 352x^3 + 352x^2 - 320x + 128	\( 5^{2}\cdot 7^{2}\cdot 577^{6} \)	14T28	$[3]$
14.0.46493802010200358912.1	x^14 + 15x^12 + 83x^10 + 214x^8 + 278x^6 + 183x^4 + 58x^2 + 7	\( -\,2^{14}\cdot 7\cdot 71^{2}\cdot 283583^{2} \)	14T57	$[8]$
14.2.50612760739840000000.1	x^14 - 4x^13 + 2x^12 + 24x^11 - 50x^10 + 8x^9 + 106x^8 - 176x^7 + 89x^6 + 28x^5 - 72x^4 + 24x^3 + 68x^2 - 96x + 64	\( 2^{27}\cdot 5^{7}\cdot 13^{6} \)	$D_7^2$ (as 14T13)	$[2]$
14.0.65111179469128871936.1	x^14 - 5x^12 + x^10 + 32x^8 - 69x^6 + 106x^4 - 107x^2 + 44	\( -\,2^{12}\cdot 11^{7}\cdot 13^{8} \)	14T40	$[2]$
14.0.75987588324579688448.1	x^14 - 4x^13 + 24x^11 - 2x^10 - 80x^9 - 92x^8 + 432x^7 + 1005x^6 - 796x^5 - 2308x^4 + 328x^3 + 3076x^2 - 1920x + 400	\( -\,2^{14}\cdot 173^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.84856922099409044287.1	x^14 - 4x^13 + 24x^12 - 32x^11 + 137x^10 - 54x^9 + 637x^8 - 148x^7 + 2542x^6 - 702x^5 + 4247x^4 - 755x^3 + 2028x^2 - 175x + 25	\( -\,19^{7}\cdot 37^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.89469990354509983683.1	x^14 - 6x^13 + 19x^12 - 44x^11 + 67x^10 - 83x^9 + 82x^8 - 17x^7 + 118x^6 + 162x^5 + 361x^4 + 423x^3 + 528x^2 + 405x + 171	\( -\,3^{7}\cdot 587^{6} \)	$D_{14}$ (as 14T3)	$[7]$ (GRH)
14.0.104052649942678734027.1	x^14 - x^13 + 10x^12 - 19x^11 + 22x^10 - 46x^9 + 23x^8 + 223x^7 - 394x^6 - 152x^5 + 734x^4 - 191x^3 - 473x^2 + 185x + 169	\( -\,3^{19}\cdot 547^{4} \)	$A_7\times C_2$ (as 14T47)	$[2, 2]$
14.0.122975574173606802987.1	x^14 - 3x^13 - 2x^12 + 3x^11 + 29x^10 + 25x^9 - 69x^8 - 93x^7 + 579x^6 + 1357x^5 + 2826x^4 + 2263x^3 + 2130x^2 + 494x + 361	\( -\,3^{15}\cdot 29^{4}\cdot 59^{4} \)	$A_7\times C_2$ (as 14T47)	$[2]$
14.0.125003362773881021207.1	x^14 - 2x^13 + 15x^12 + 8x^11 + 80x^10 + 108x^9 + 519x^8 + 608x^7 + 2679x^6 + 1744x^5 + 3438x^4 + 1127x^3 + 1067x^2 + 170x + 25	\( -\,743^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.222902399220465737943.1	x^14 - 2x^13 - 5x^12 + 35x^11 + 5x^10 - 193x^9 + 415x^8 + 241x^7 - 440x^6 - 357x^5 + 3537x^4 - 639x^3 + 2781x^2 + 7209x + 7587	\( -\,3^{7}\cdot 269^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.249430673908303812379.1	x^14 - 3x^13 + 26x^10 + 65x^6 + 39x^5 + 52x^2 + 36x + 9	\( -\,7^{7}\cdot 13^{13} \)	$D_{14}$ (as 14T3)	$[2]$
14.0.273657381125642667711.1	x^14 - 6x^13 + 21x^12 - 63x^11 + 72x^10 + 162x^9 - 578x^8 + 876x^7 - 510x^6 - 2556x^5 + 7677x^4 - 8370x^3 + 4195x^2 - 1707x + 867	\( -\,3^{7}\cdot 277^{7} \)	$D_{7}$ (as 14T2)	$[4]$
14.2.276805072512186768589.1	x^14 - 5x^13 + 20x^12 - 33x^11 + 30x^10 + 103x^9 - 244x^8 + 419x^7 - 149x^6 + 153x^5 - 73x^4 + 101x^3 - 55x^2 + 16x - 1	\( 13\cdot 577^{7} \)	14T38	$[6]$
14.0.356513163590850929567.1	x^14 - 6x^13 + 19x^12 - 70x^11 + 212x^10 - 467x^9 + 1126x^8 - 2393x^7 + 5781x^6 - 11969x^5 + 20359x^4 - 32768x^3 + 36718x^2 - 35471x + 26759	\( -\,863^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.413780909272912101376.1	x^14 + 17x^12 + 106x^10 + 304x^8 + 419x^6 + 259x^4 + 59x^2 + 1	\( -\,2^{20}\cdot 4457^{4} \)	14T43	$[2, 4]$
14.0.474589190351997996299.1	x^14 + 4x^12 + 40x^10 + 54x^8 + 288x^6 + 3272x^4 + 7273x^2 + 3596	\( -\,29^{7}\cdot 31^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.6.532317447138820708825.3	x^14 - x^13 - 6x^12 + 37x^11 - 79x^10 + 60x^9 + 24x^8 - 233x^7 + 342x^6 - 160x^5 + 10x^4 + 15x^3 - 5x^2 - 7x + 1	\( 5^{2}\cdot 577^{7} \)	14T27	$[2]$
14.0.624714053801881484375.1	x^14 + 16x^12 - 70x^10 + 15x^8 + 95x^6 + 101x^4 + 166x^2 + 935	\( -\,5^{7}\cdot 11^{7}\cdot 17^{7} \)	$D_{7}$ (as 14T2)	$[2, 2]$ (GRH)
14.0.637206919404798869504.1	x^14 + 14x^12 + 84x^10 + 280x^8 + 560x^6 + 672x^4 + 448x^2 + 126	\( -\,2^{27}\cdot 7^{15} \)	$F_7 \times C_2$ (as 14T7)	$[4]$
14.0.773792930870360792667.1	x^14 - x^13 + 13x^12 - 2x^11 + 123x^10 - 42x^9 + 353x^8 - 132x^7 + 776x^6 - 254x^5 + 455x^4 + 182x^3 + 67x^2 + 9x + 1	\( -\,3^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2]$
14.0.845634697317927878656.1	x^14 + 16x^12 + 96x^10 + 272x^8 + 376x^6 + 236x^4 + 60x^2 + 4	\( -\,2^{20}\cdot 73^{8} \)	$(C_7:C_3) \times C_2$ (as 14T5)	$[8]$
14.0.890538686357276796875.1	x^14 - 7x^13 + 14x^12 + 7x^11 - 21x^10 - 126x^9 + 7x^8 + 471x^7 + 1274x^6 - 287x^5 - 3171x^4 - 1498x^3 + 2576x^2 + 1960x + 400	\( -\,5^{7}\cdot 7^{19} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.2.1000402691469045597184.1	x^14 + 14x^12 + 72x^10 + 168x^8 + 177x^6 + 59x^4 - 15x^2 - 4	\( 2^{10}\cdot 149^{4}\cdot 211^{4} \)	14T53	$[2]$