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Results (displaying all 23 matches)

Label Polynomial Discriminant Galois group Class group
18.0.10383286663954563863.1 x18 - 4x17 + 11x16 - 22x15 + 36x14 - 53x13 + 80x12 - 116x11 + 154x10 - 173x9 + 154x8 - 116x7 + 80x6 - 53x5 + 36x4 - 22x3 + 11x2 - 4x + 1 \( -\,7^{8}\cdot 23^{9} \) $D_9:C_3$ (as 18T18) Trivial
18.0.24417546297445042591.1 x18 - 5x17 + 12x16 - 12x15 - 13x14 + 66x13 - 110x12 + 88x11 + 15x10 - 143x9 + 225x8 - 238x7 + 205x6 - 155x5 + 102x4 - 54x3 + 22x2 - 6x + 1 \( -\,31^{13} \) $D_9:C_3$ (as 18T18) Trivial
18.0.364318593289782755328.1 x18 - 6x12 - 4x9 + 36x6 + 12x3 + 4 \( -\,2^{16}\cdot 3^{33} \) $D_9:C_3$ (as 18T18) Trivial
18.0.19383245667680019896796723.2 x18 + 3 \( -\,3^{53} \) $D_9:C_3$ (as 18T18) Trivial
18.18.28195670721946845353167339457.1 x18 - 33x16 - 11x15 + 387x14 + 144x13 - 2216x12 - 623x11 + 6888x10 + 821x9 - 11951x8 + 859x7 + 11003x6 - 2794x5 - 4431x4 + 1723x3 + 391x2 - 150x - 9 \( 7^{8}\cdot 257^{9} \) $D_9:C_3$ (as 18T18) Trivial (GRH)
18.18.144651937430092424868603953152.1 x18 - 9x17 + 3x16 + 180x15 - 362x14 - 1330x13 + 3998x12 + 4144x11 - 19161x10 - 2623x9 + 45321x8 - 13752x7 - 49858x6 + 29002x5 + 18518x4 - 16692x3 + 1755x2 + 865x - 137 \( 2^{16}\cdot 19^{8}\cdot 37^{9} \) $D_9:C_3$ (as 18T18) Trivial (GRH)
18.0.17582592502916589732558131885417583280128.1 x18 - 9x17 + 45x16 - 156x15 + 414x14 - 882x13 + 1554x12 - 2304x11 + 2907x10 + 107993x9 - 497187x8 - 2002680x7 + 9336642x6 - 7002198x5 - 7000902x4 + 9334932x3 - 2000331x2 - 500103x + 3087691489 \( -\,2^{16}\cdot 3^{53}\cdot 7^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 3]$ (GRH)
18.0.17582592502916589732558131885417583280128.2 x18 + 114354828 \( -\,2^{16}\cdot 3^{53}\cdot 7^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 6, 6]$ (GRH)
18.0.769445538694487691557611230000000000000000.1 x18 - 9x17 + 39x16 - 108x15 + 234x14 - 462x13 - 4710x12 + 32004x11 - 33261x10 - 132499x9 + 4397733x8 - 16434924x7 - 77689590x6 + 289673118x5 + 666797838x4 - 1835112552x3 - 3082794183x2 + 4051301331x + 6652087267 \( -\,2^{16}\cdot 3^{33}\cdot 5^{16}\cdot 7^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 3, 9, 9]$ (GRH)
18.0.769445538694487691557611230000000000000000.2 x18 + 3x16 - 36x14 - 5628x12 - 31914x10 + 1031922x8 + 14934396x6 + 76305348x4 + 153013329x2 + 52743747 \( -\,2^{16}\cdot 3^{33}\cdot 5^{16}\cdot 7^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 9, 36, 36]$ (GRH)
18.0.29595566572540406594298039314351025668947968.1 x18 + 18766633392 \( -\,2^{16}\cdot 3^{53}\cdot 13^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3]$ (GRH)
18.0.29595566572540406594298039314351025668947968.2 x18 - 9x17 + 45x16 - 156x15 + 414x14 - 882x13 + 1554x12 - 2304x11 + 2907x10 + 418685x9 - 1895301x8 - 7595136x7 + 35434770x6 - 26575794x5 - 26574498x4 + 35433060x3 - 7592787x2 - 1898217x + 44484293569 \( -\,2^{16}\cdot 3^{53}\cdot 13^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3]$ (GRH)
18.0.1674839540438459282902886554720879596051603468288.1 x18 - 9x17 + 39x16 - 108x15 + 207x14 - 273x13 - 2436x12 + 15903x11 - 106503x10 + 385808x9 - 162243x8 - 1489695x7 + 36908697x6 - 104067936x5 + 573490734x4 - 975956418x3 + 3278636388x2 - 2807652156x + 5898348532 \( -\,2^{12}\cdot 3^{33}\cdot 7^{16}\cdot 19^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 3, 3, 3, 9, 9]$ (GRH)
18.0.167680668858686349225598639349151451875000000000000.1 x18 + 903544320000 \( -\,2^{12}\cdot 3^{53}\cdot 5^{16}\cdot 7^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 3, 3, 6, 6]$ (GRH)
18.0.167680668858686349225598639349151451875000000000000.2 x18 + 658683809280000 \( -\,2^{12}\cdot 3^{53}\cdot 5^{16}\cdot 7^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 3, 3, 6, 6]$ (GRH)
18.0.1818280032576028549434598701257820007683011156717568.1 x18 + 29056171447488 \( -\,2^{12}\cdot 3^{53}\cdot 73^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 3, 3, 3, 9]$ (GRH)
18.0.429012268162007190724164051226024049904030000000000000000.1 x18 + 17862732942187500 \( -\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 19^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 9, 9, 9]$ (GRH)
18.0.429012268162007190724164051226024049904030000000000000000.2 x18 + 73165754131200 \( -\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 19^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 9, 18, 18]$ (GRH)
18.0.152674612414621913640596447375544095872332030000000000000000.1 x18 - 9x17 + 45x16 - 156x15 + 414x14 - 882x13 + 1554x12 - 2304x11 + 2907x10 + 223429361x9 - 1005443343x8 - 4021787304x7 + 18768331554x6 - 14076248382x5 - 14076247086x4 + 18768329844x3 - 4021784955x2 - 1005446259x + 12480520737495001 \( -\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 31^{12} \) $D_9:C_3$ (as 18T18) n/a
18.0.152674612414621913640596447375544095872332030000000000000000.2 x18 - 9x17 + 45x16 - 156x15 + 414x14 - 882x13 + 1554x12 - 2304x11 + 2907x10 + 386088221x9 - 1737408213x8 - 6949646784x7 + 32431675794x6 - 24323756562x5 - 24323755266x4 + 32431674084x3 - 6949644435x2 - 1737411129x + 37266634952753761 \( -\,2^{16}\cdot 3^{53}\cdot 5^{16}\cdot 31^{12} \) $D_9:C_3$ (as 18T18) $[3, 3, 3, 3, 3, 3, 9]$ (GRH)
18.0.1686927965605508492466881426820189615618051032124693313927446528.1 x18 + 1233198609603674112 \( -\,2^{16}\cdot 3^{53}\cdot 7^{16}\cdot 43^{12} \) $D_9:C_3$ (as 18T18) n/a
18.0.345440062370637727263683997009662531824823720642870008633255723008.1 x18 + 6257694863834800428 \( -\,2^{16}\cdot 3^{53}\cdot 7^{16}\cdot 67^{12} \) $D_9:C_3$ (as 18T18) n/a
18.0.83221605475299746491196195815324545938996983211283813572975383538761728.1 x18 + 110960891811846912 \( -\,2^{16}\cdot 3^{53}\cdot 11^{16}\cdot 103^{12} \) $D_9:C_3$ (as 18T18) n/a


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