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Label Polynomial Discriminant Galois group Class group
45.15.174...691.1 x45 - 12x44 + 42x43 + 36x42 - 525x41 + 702x40 + 2050x39 - 5802x38 - 2832x37 + 26919x36 - 20811x35 - 75546x34 + 201699x33 - 97125x32 - 532302x31 + 1289591x30 - 477339x29 - 2405610x28 + 4128988x27 - 1666824x26 - 5259345x25 + 9273382x24 + 3749217x23 - 15223818x22 - 9661128x21 + 33692574x20 - 4282803x19 - 38096273x18 + 36480543x17 - 14154921x16 + 10925288x15 - 437979x14 - 36804246x13 + 57064132x12 - 25852146x11 - 34300866x10 + 48986404x9 - 2084457x8 - 23365995x7 + 5433983x6 + 5348430x5 - 1230861x4 - 665734x3 + 68376x2 + 38973x + 2969 \( -\,3^{60}\cdot 11^{39} \) $C_{15}\times S_3$ (as 45T3) trivial (GRH)
45.15.226...891.1 x45 - 3x44 + 19x43 - 46x42 + 57x41 - 164x40 - 1542x39 + 2752x38 - 13177x37 + 27636x36 - 5513x35 + 194674x34 - 95004x33 + 1568504x32 - 4411428x31 + 7701411x30 - 22788169x29 + 356245x28 + 13001022x27 - 120681074x26 + 379138834x25 - 251876102x24 + 576442931x23 + 394617661x22 - 1914308187x21 + 1873927920x20 - 5326366508x19 + 1371219529x18 + 2001539759x17 - 9889048234x16 + 22330230077x15 - 9918095549x14 + 1934927850x13 + 41001461054x12 - 37979697765x11 + 8169529015x10 + 13175783912x9 - 55418628407x8 + 2188320806x7 - 1793697518x6 - 21729183123x5 - 927541692x4 + 301468299x3 + 1484196634x2 + 59977427x - 879691 \( -\,11^{39}\cdot 31^{30} \) $C_{15}\times S_3$ (as 45T3) n/a
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