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 all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.1737547626496854250169.1	x^18 - 5x^16 - 6x^15 + 10x^14 + 25x^13 + 3x^12 - 40x^11 - 39x^10 + 16x^9 + 55x^8 + 28x^7 - 22x^6 - 35x^5 - 14x^4 + 6x^3 + 10x^2 + 5x + 1	\( 7^{12}\cdot 13^{3}\cdot 57138677 \)	18T926	Trivial
18.12.168734674063693863788947291.1	x^18 - 9x^16 - 6x^15 + 28x^14 + 45x^13 - 18x^12 - 112x^11 - 83x^10 + 79x^9 + 174x^8 + 76x^7 - 85x^6 - 118x^5 - 38x^4 + 27x^3 + 28x^2 + 9x + 1	\( -\,7^{12}\cdot 71\cdot 181^{3}\cdot 28955681 \)	18T926	Trivial (GRH)
18.14.3157637250396545217942712001.1	x^18 - 16x^16 - 6x^15 + 101x^14 + 80x^13 - 302x^12 - 404x^11 + 348x^10 + 931x^9 + 233x^8 - 856x^7 - 853x^6 - 31x^5 + 428x^4 + 311x^3 + 101x^2 + 16x + 1	\( 7^{12}\cdot 43\cdot 181^{3}\cdot 894708527 \)	18T926	Trivial (GRH)
18.16.44202745482204952292385377971.1	x^18 - 21x^16 - 6x^15 + 178x^14 + 105x^13 - 762x^12 - 712x^11 + 1627x^10 + 2311x^9 - 1158x^8 - 3464x^7 - 1237x^6 + 1514x^5 + 1732x^4 + 771x^3 + 178x^2 + 21x + 1	\( -\,7^{12}\cdot 71\cdot 181^{3}\cdot 7585403561 \)	18T926	Trivial (GRH)
18.4.577673953978573690445376000000.1	x^18 + 18x^14 - 24x^13 + 8x^12 - 243x^10 + 648x^9 - 648x^8 + 288x^7 - 3693x^6 + 14580x^5 - 24300x^4 + 21600x^3 - 10800x^2 + 2880x - 320	\( -\,2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{12} \)	18T926	Trivial (GRH)
18.18.1839619942606602339050600799157.1	x^18 - 23x^16 - 6x^15 + 213x^14 + 115x^13 - 1002x^12 - 852x^11 + 2413x^10 + 3031x^9 - 2273x^8 - 5056x^7 - 1105x^6 + 2699x^5 + 2528x^4 + 1011x^3 + 213x^2 + 23x + 1	\( 7^{12}\cdot 13^{3}\cdot 29^{3}\cdot 223\cdot 1051\cdot 10583273 \)	18T926	Trivial (GRH)
18.8.39997499095444517159888896524288.1	x^18 - 18x^16 - 12x^15 + 135x^14 + 180x^13 - 485x^12 - 1080x^11 + 555x^10 + 3120x^9 + 1512x^8 - 3780x^7 - 5155x^6 - 324x^5 + 4119x^4 + 3464x^3 + 504x^2 - 672x - 16	\( -\,2^{17}\cdot 3^{18}\cdot 31^{12} \)	18T926	Trivial (GRH)
18.4.159989996381778068639555586097152.1	x^18 - 18x^16 - 7x^15 + 135x^14 + 105x^13 - 574x^12 - 630x^11 + 1623x^10 + 1514x^9 - 3294x^8 + 549x^7 + 3697x^6 - 8451x^5 + 1470x^4 + 6648x^3 - 6336x^2 + 10512x - 2848	\( -\,2^{19}\cdot 3^{18}\cdot 31^{12} \)	18T926	Trivial (GRH)
18.8.2366152515496237836064260096000000.1	x^18 - 12x^16 - 8x^15 - 18x^14 - 24x^13 + 502x^12 + 1188x^11 - 363x^10 - 2376x^9 - 4662x^8 - 18684x^7 - 14887x^6 + 44820x^5 + 86280x^4 + 9280x^3 - 39600x^2 - 14400x + 8000	\( -\,2^{24}\cdot 3^{18}\cdot 5^{6}\cdot 13^{12} \)	18T926	Trivial (GRH)
18.6.32466386978047110069722084989206528.1	x^18 - 18x^16 - 12x^15 + 135x^14 + 180x^13 - 516x^12 - 1080x^11 + 927x^10 + 3368x^9 - 162x^8 - 6012x^7 - 2743x^6 + 6372x^5 + 7224x^4 - 1472x^3 - 7920x^2 - 5952x - 512	\( 2^{21}\cdot 3^{18}\cdot 43^{12} \)	18T926	Trivial (GRH)
18.10.33566833452761315517557908483560329.1	x^18 - 8x^17 + 22x^16 - 81x^15 + 399x^14 - 864x^13 + 1676x^12 - 6019x^11 + 10241x^10 - 9962x^9 + 27064x^8 - 32454x^7 - 10007x^6 - 4076x^5 + 41523x^4 + 23494x^3 - 51973x^2 + 10933	\( 7^{12}\cdot 13\cdot 57138677^{3} \)	18T926	Trivial (GRH)
18.0.87651540491153387182800195727392768.1	x^18 + 72x^14 - 96x^13 + 32x^12 + 1539x^10 - 4104x^9 + 4104x^8 - 1824x^7 + 9781x^6 - 37908x^5 + 63180x^4 - 56160x^3 + 28080x^2 - 7488x + 832	\( -\,2^{30}\cdot 3^{18}\cdot 7^{12}\cdot 13^{5}\cdot 41 \)	18T926	$[2]$ (GRH)
18.6.129865547912188440278888339956826112.1	x^18 - 18x^16 - 24x^15 + 135x^14 + 360x^13 - 952x^12 - 2160x^11 + 6159x^10 + 7376x^9 - 23706x^8 - 17784x^7 + 41945x^6 + 30024x^5 - 13692x^4 - 9984x^3 - 29520x^2 - 42624x - 11072	\( 2^{23}\cdot 3^{18}\cdot 43^{12} \)	18T926	Trivial (GRH)
18.12.871847571394253513930693071110930432.1	x^18 - 48x^16 - 32x^15 + 918x^14 + 1224x^13 - 8986x^12 - 17820x^11 + 46281x^10 + 128312x^9 - 106974x^8 - 491964x^7 + 15065x^6 + 985140x^5 + 310128x^4 - 1003392x^3 - 316368x^2 + 616512x - 140608	\( -\,2^{30}\cdot 3^{18}\cdot 7^{12}\cdot 13^{3}\cdot 41^{3} \)	18T926	Trivial (GRH)
18.2.420337214415108488729153861721645907968.1	x^18 - 24x^16 - 68x^15 + 54x^14 - 48x^13 - 926x^12 + 4500x^11 + 5175x^10 - 15140x^9 - 36108x^8 - 36432x^7 + 184739x^6 - 286776x^5 + 215448x^4 - 64832x^3 - 44352x^2 + 16896x + 5632	\( 2^{30}\cdot 3^{18}\cdot 7^{3}\cdot 11^{3}\cdot 19^{12} \)	18T926	$[2]$ (GRH)
18.10.1037975570290369941555665658537125609472.1	x^18 - 90x^14 - 120x^13 - 40x^12 + 2187x^10 + 5832x^9 + 5832x^8 + 2592x^7 - 7587x^6 - 32076x^5 - 53460x^4 - 47520x^3 - 23760x^2 - 6336x - 704	\( 2^{30}\cdot 3^{18}\cdot 7\cdot 11^{5}\cdot 19^{12} \)	18T926	Trivial (GRH)
18.0.21768647730913562905265507945105445204931.1	x^18 - 2x^17 - 3x^16 + 69x^15 - 187x^14 - 4x^13 + 2973x^12 - 9432x^11 + 8083x^10 + 44326x^9 - 142708x^8 + 103572x^7 + 826339x^6 - 2306607x^5 + 2772355x^4 + 798147x^3 + 9473184x^2 + 72067141	\( -\,7^{12}\cdot 71^{3}\cdot 181\cdot 28955681^{3} \)	18T926	$[3374]$ (GRH)
18.6.142660962891827847357688087745406439211942561.1	x^18 - 108x^16 - 81x^15 + 4482x^14 + 7290x^13 - 87018x^12 - 242028x^11 + 634635x^10 + 3595266x^9 + 3818016x^8 - 19473048x^7 - 93602247x^6 - 62244207x^5 + 469197468x^4 + 921309390x^3 + 291125718x^2 - 546084423x - 989652329	\( 7^{12}\cdot 43^{3}\cdot 181\cdot 894708527^{3} \)	18T926	Trivial (GRH)
18.12.391350753932783462782732212010334985869953357771.1	x^18 - 186x^16 - 81x^15 + 14373x^14 + 12555x^13 - 592021x^12 - 776142x^11 + 13734798x^10 + 24094476x^9 - 170197830x^8 - 381679857x^7 + 865071579x^6 + 2627021727x^5 + 630219135x^4 - 3114283707x^3 - 7378892694x^2 - 3895392708x + 7892777521	\( -\,7^{12}\cdot 71^{3}\cdot 181\cdot 7585403561^{3} \)	18T926	Trivial (GRH)
18.18.79634372972300794853892771897752194830441843575053.1	x^18 - 234x^16 - 81x^15 + 22437x^14 + 15795x^13 - 1144536x^12 - 1211598x^11 + 33557994x^10 + 46678194x^9 - 565874667x^8 - 947632203x^7 + 5143953720x^6 + 9562968054x^5 - 21792576465x^4 - 39404619099x^3 + 38964745521x^2 + 50872628097x - 25675621091	\( 7^{12}\cdot 13\cdot 29\cdot 223^{3}\cdot 1051^{3}\cdot 10583273^{3} \)	18T926	Trivial (GRH)