Fungrim entry: 20b6d2

Table of

H_{D}\!\left(x\right)

for

-D \le 68

$D$	$H_{D}\!\left(x\right)$
-3	$x$
-4	$x - 1728$
-7	$x + 3375$
-8	$x - 8000$
-11	$x + 32768$
-12	$x - 54000$
-15	${x}^{2} + 191025 x - 121287375$
-16	$x - 287496$
-19	$x + 884736$
-20	${x}^{2} - 1264000 x - 681472000$
-23	${x}^{3} + 3491750 {x}^{2} - 5151296875 x + 12771880859375$
-24	${x}^{2} - 4834944 x + 14670139392$
-27	$x + 12288000$
-28	$x - 16581375$
-31	${x}^{3} + 39491307 {x}^{2} - 58682638134 x + 1566028350940383$
-32	${x}^{2} - 52250000 x + 12167000000$
-35	${x}^{2} + 117964800 x - 134217728000$
-36	${x}^{2} - 153542016 x - 1790957481984$
-39	${x}^{4} + 331531596 {x}^{3} - 429878960946 {x}^{2} + 109873509788637459 x + 20919104368024767633$
-40	${x}^{2} - 425692800 x + 9103145472000$
-43	$x + 884736000$
-44	${x}^{3} - 1122662608 {x}^{2} + 270413882112 x - 653249011576832$
-47	${x}^{5} + 2257834125 {x}^{4} - 9987963828125 {x}^{3} + 5115161850595703125 {x}^{2} - 14982472850828613281250 x + 16042929600623870849609375$
-48	${x}^{2} - 2835810000 x + 6549518250000$
-51	${x}^{2} + 5541101568 x + 6262062317568$
-52	${x}^{2} - 6896880000 x - 567663552000000$
-55	${x}^{4} + 13136684625 {x}^{3} - 20948398473375 {x}^{2} + 172576736359017890625 x - 18577989025032784359375$
-56	${x}^{4} - 16220384512 {x}^{3} + 2059647197077504 {x}^{2} + 2257767342088912896 x + 10064086044321563803648$
-59	${x}^{3} + 30197678080 {x}^{2} - 140811576541184 x + 374643194001883136$
-60	${x}^{2} - 37018076625 x + 153173312762625$
-63	${x}^{4} + 67515199875 {x}^{3} - 193068841781250 {x}^{2} + 4558451243295023437500 x - 6256903954262253662109375$
-64	${x}^{2} - 82226316240 x - 7367066619912$
-67	$x + 147197952000$
-68	${x}^{4} - 178211040000 {x}^{3} - 75843692160000000 {x}^{2} - 318507038720000000000 x - 2089297506304000000000000$

Table data:

\left(D, p\right)

such that

H_{D}\!\left(x\right) = p

Assumptions:

x \in \mathbb{C}

TeX:

x \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`HilbertClassPolynomial`	$H_{D}\!\left(x\right)$	Hilbert class polynomial
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	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)))

Topics using this entry

Modular j-invariant