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Label Polynomial Discriminant Galois group Class group
23.23.611...809.1 x23 - x22 - 22x21 + 21x20 + 210x19 - 190x18 - 1140x17 + 969x16 + 3876x15 - 3060x14 - 8568x13 + 6188x12 + 12376x11 - 8008x10 - 11440x9 + 6435x8 + 6435x7 - 3003x6 - 2002x5 + 715x4 + 286x3 - 66x2 - 12x + 1 \( 47^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.140...521.1 x23 - x22 - 66x21 + 147x20 + 1630x19 - 5648x18 - 16457x17 + 92686x16 + 18441x15 - 709360x14 + 832638x13 + 2239299x12 - 5679764x11 - 156443x10 + 12673530x9 - 11318727x8 - 6468097x7 + 14166332x6 - 3186420x5 - 5386949x4 + 2918745x3 + 436718x2 - 516219x + 63941 \( 139^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.542...529.1 x23 - x22 - 132x21 + 269x20 + 6722x19 - 19118x18 - 167488x17 + 601226x16 + 2127300x15 - 9664345x14 - 12698450x13 + 83446410x12 + 19888027x11 - 390244377x10 + 110929757x9 + 994369765x8 - 511651057x7 - 1370318108x6 + 775297206x5 + 972267257x4 - 466392148x3 - 312747839x2 + 85444683x + 38737459 \( 277^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.399...721.1 x23 - x22 - 220x21 + 87x20 + 19764x19 + 7502x18 - 942100x17 - 1247222x16 + 25503060x15 + 62076437x14 - 368245290x13 - 1464919087x12 + 1795768610x11 + 16428532486x10 + 16509241674x9 - 60887740509x8 - 181108379413x7 - 148388500129x6 + 88587002490x5 + 252590462192x4 + 171337144724x3 + 31220491402x2 - 10221385976x - 3012210881 \( 461^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.824...241.1 x23 - 253x21 - 161x20 + 26335x19 + 33028x18 - 1467515x17 - 2734079x16 + 47658093x15 + 118763283x14 - 910024555x13 - 2931964974x12 + 9516128606x11 + 41347298260x10 - 39738537224x9 - 313669878607x8 - 104709853475x7 + 1076728692839x6 + 1230914947669x5 - 913297744524x4 - 1823221987393x3 - 124828056170x2 + 645413252986x + 157112485811 \( 23^{44} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.126...801.1 x23 - x22 - 286x21 + 61x20 + 32489x19 + 14967x18 - 1928206x17 - 2239956x16 + 65439786x15 + 128285990x14 - 1279328514x13 - 3758213062x12 + 12892455511x11 + 58719404143x10 - 31105194350x9 - 448954503771x8 - 491325793721x7 + 1084631540509x6 + 3053149451318x5 + 2305895458302x4 - 281144721703x3 - 1007901237378x2 - 154197339893x + 118359867167 \( 599^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.294...281.1 x23 - x22 - 330x21 + 491x20 + 46010x19 - 87998x18 - 3534734x17 + 8097381x16 + 163274386x15 - 432276476x14 - 4617725871x13 + 13958868541x12 + 76934101895x11 - 269759119969x10 - 654647210801x9 + 2901393808025x8 + 1396549312920x7 - 14112769866979x6 + 10842020004862x5 + 12214116095559x4 - 17293268074281x3 + 3381350907752x2 + 1669609496979x - 220900980203 \( 691^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.161...641.1 x23 - x22 - 396x21 + 517x20 + 58242x19 - 89048x18 - 4136665x17 + 6675371x16 + 155317993x15 - 248917597x14 - 3168505860x13 + 4803054368x12 + 34789513687x11 - 47690452504x10 - 193631555469x9 + 225956060874x8 + 483028561517x7 - 415966978205x6 - 465412635150x5 + 267147031000x4 + 115014666875x3 - 62643096875x2 - 1127109375x + 2017578125 \( 829^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
23.23.477...489.1 x23 - x22 - 462x21 + 519x20 + 78046x19 - 96292x18 - 6163501x17 + 7373917x16 + 250455980x15 - 290053856x14 - 5501340108x13 + 6875865393x12 + 66926124686x11 - 96263348909x10 - 438046106473x9 + 740824871406x8 + 1383038185176x7 - 2863260767644x6 - 1570567685623x5 + 5193710248505x4 - 862947136357x3 - 3368621429671x2 + 2154713129200x - 341763031283 \( 967^{22} \) $C_{23}$ (as 23T1) trivial (GRH)
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