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Fungrim entry: 20b6d2

Table of HD ⁣(x)H_{D}\!\left(x\right) for D68-D \le 68
DD HD ⁣(x)H_{D}\!\left(x\right)
-3xx
-4x1728x - 1728
-7x+3375x + 3375
-8x8000x - 8000
-11x+32768x + 32768
-12x54000x - 54000
-15x2+191025x121287375{x}^{2} + 191025 x - 121287375
-16x287496x - 287496
-19x+884736x + 884736
-20x21264000x681472000{x}^{2} - 1264000 x - 681472000
-23x3+3491750x25151296875x+12771880859375{x}^{3} + 3491750 {x}^{2} - 5151296875 x + 12771880859375
-24x24834944x+14670139392{x}^{2} - 4834944 x + 14670139392
-27x+12288000x + 12288000
-28x16581375x - 16581375
-31x3+39491307x258682638134x+1566028350940383{x}^{3} + 39491307 {x}^{2} - 58682638134 x + 1566028350940383
-32x252250000x+12167000000{x}^{2} - 52250000 x + 12167000000
-35x2+117964800x134217728000{x}^{2} + 117964800 x - 134217728000
-36x2153542016x1790957481984{x}^{2} - 153542016 x - 1790957481984
-39x4+331531596x3429878960946x2+109873509788637459x+20919104368024767633{x}^{4} + 331531596 {x}^{3} - 429878960946 {x}^{2} + 109873509788637459 x + 20919104368024767633
-40x2425692800x+9103145472000{x}^{2} - 425692800 x + 9103145472000
-43x+884736000x + 884736000
-44x31122662608x2+270413882112x653249011576832{x}^{3} - 1122662608 {x}^{2} + 270413882112 x - 653249011576832
-47x5+2257834125x49987963828125x3+5115161850595703125x214982472850828613281250x+16042929600623870849609375{x}^{5} + 2257834125 {x}^{4} - 9987963828125 {x}^{3} + 5115161850595703125 {x}^{2} - 14982472850828613281250 x + 16042929600623870849609375
-48x22835810000x+6549518250000{x}^{2} - 2835810000 x + 6549518250000
-51x2+5541101568x+6262062317568{x}^{2} + 5541101568 x + 6262062317568
-52x26896880000x567663552000000{x}^{2} - 6896880000 x - 567663552000000
-55x4+13136684625x320948398473375x2+172576736359017890625x18577989025032784359375{x}^{4} + 13136684625 {x}^{3} - 20948398473375 {x}^{2} + 172576736359017890625 x - 18577989025032784359375
-56x416220384512x3+2059647197077504x2+2257767342088912896x+10064086044321563803648{x}^{4} - 16220384512 {x}^{3} + 2059647197077504 {x}^{2} + 2257767342088912896 x + 10064086044321563803648
-59x3+30197678080x2140811576541184x+374643194001883136{x}^{3} + 30197678080 {x}^{2} - 140811576541184 x + 374643194001883136
-60x237018076625x+153173312762625{x}^{2} - 37018076625 x + 153173312762625
-63x4+67515199875x3193068841781250x2+4558451243295023437500x6256903954262253662109375{x}^{4} + 67515199875 {x}^{3} - 193068841781250 {x}^{2} + 4558451243295023437500 x - 6256903954262253662109375
-64x282226316240x7367066619912{x}^{2} - 82226316240 x - 7367066619912
-67x+147197952000x + 147197952000
-68x4178211040000x375843692160000000x2318507038720000000000x2089297506304000000000000{x}^{4} - 178211040000 {x}^{3} - 75843692160000000 {x}^{2} - 318507038720000000000 x - 2089297506304000000000000
Table data: (D,p)\left(D, p\right) such that HD ⁣(x)=pH_{D}\!\left(x\right) = p
Assumptions:xCx \in \mathbb{C}
TeX:
x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
HilbertClassPolynomialHD ⁣(x)H_{D}\!\left(x\right) Hilbert class polynomial
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("20b6d2"),
    Description("Table of", HilbertClassPolynomial(D, x), "for", LessEqual(Neg(D), 68)),
    Table(TableRelation(Tuple(D, p), Equal(HilbertClassPolynomial(D, x), p)), TableHeadings(D, HilbertClassPolynomial(D, x)), TableSplit(1), List(Tuple(-3, x), Tuple(-4, Sub(x, 1728)), Tuple(-7, Add(x, 3375)), Tuple(-8, Sub(x, 8000)), Tuple(-11, Add(x, 32768)), Tuple(-12, Sub(x, 54000)), Tuple(-15, Sub(Add(Pow(x, 2), Mul(191025, x)), 121287375)), Tuple(-16, Sub(x, 287496)), Tuple(-19, Add(x, 884736)), Tuple(-20, Sub(Sub(Pow(x, 2), Mul(1264000, x)), 681472000)), Tuple(-23, Add(Sub(Add(Pow(x, 3), Mul(3491750, Pow(x, 2))), Mul(5151296875, x)), 12771880859375)), Tuple(-24, Add(Sub(Pow(x, 2), Mul(4834944, x)), 14670139392)), Tuple(-27, Add(x, 12288000)), Tuple(-28, Sub(x, 16581375)), Tuple(-31, Add(Sub(Add(Pow(x, 3), Mul(39491307, Pow(x, 2))), Mul(58682638134, x)), 1566028350940383)), Tuple(-32, Add(Sub(Pow(x, 2), Mul(52250000, x)), 12167000000)), Tuple(-35, Sub(Add(Pow(x, 2), Mul(117964800, x)), 134217728000)), Tuple(-36, Sub(Sub(Pow(x, 2), Mul(153542016, x)), 1790957481984)), Tuple(-39, Add(Add(Sub(Add(Pow(x, 4), Mul(331531596, Pow(x, 3))), Mul(429878960946, Pow(x, 2))), Mul(109873509788637459, x)), 20919104368024767633)), Tuple(-40, Add(Sub(Pow(x, 2), Mul(425692800, x)), 9103145472000)), Tuple(-43, Add(x, 884736000)), Tuple(-44, Sub(Add(Sub(Pow(x, 3), Mul(1122662608, Pow(x, 2))), Mul(270413882112, x)), 653249011576832)), Tuple(-47, Add(Sub(Add(Sub(Add(Pow(x, 5), Mul(2257834125, Pow(x, 4))), Mul(9987963828125, Pow(x, 3))), Mul(5115161850595703125, Pow(x, 2))), Mul(14982472850828613281250, x)), 16042929600623870849609375)), Tuple(-48, Add(Sub(Pow(x, 2), Mul(2835810000, x)), 6549518250000)), Tuple(-51, Add(Add(Pow(x, 2), Mul(5541101568, x)), 6262062317568)), Tuple(-52, Sub(Sub(Pow(x, 2), Mul(6896880000, x)), 567663552000000)), Tuple(-55, Sub(Add(Sub(Add(Pow(x, 4), Mul(13136684625, Pow(x, 3))), Mul(20948398473375, Pow(x, 2))), Mul(172576736359017890625, x)), 18577989025032784359375)), Tuple(-56, Add(Add(Add(Sub(Pow(x, 4), Mul(16220384512, Pow(x, 3))), Mul(2059647197077504, Pow(x, 2))), Mul(2257767342088912896, x)), 10064086044321563803648)), Tuple(-59, Add(Sub(Add(Pow(x, 3), Mul(30197678080, Pow(x, 2))), Mul(140811576541184, x)), 374643194001883136)), Tuple(-60, Add(Sub(Pow(x, 2), Mul(37018076625, x)), 153173312762625)), Tuple(-63, Sub(Add(Sub(Add(Pow(x, 4), Mul(67515199875, Pow(x, 3))), Mul(193068841781250, Pow(x, 2))), Mul(4558451243295023437500, x)), 6256903954262253662109375)), Tuple(-64, Sub(Sub(Pow(x, 2), Mul(82226316240, x)), 7367066619912)), Tuple(-67, Add(x, 147197952000)), Tuple(-68, Sub(Sub(Sub(Sub(Pow(x, 4), Mul(178211040000, Pow(x, 3))), Mul(75843692160000000, Pow(x, 2))), Mul(318507038720000000000, x)), 2089297506304000000000000)))),
    Variables(x),
    Assumptions(Element(x, CC)))

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2019-09-20 18:07:53.062439 UTC