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Modular polynomials for Weber's ƒ-function
This page lists the modular polynomials Φℓ(X,Y) between ƒ(z) and ƒ(z ⁄ ℓ) for primes ℓ < 5000.
The Weber ƒ-function is related to the j-function via: j = (ƒ24-16)3⁄ ƒ24.
Each file is an ascii text file with a line for each non-zero coefficient of Φℓ(X,Y).
For example, the file listing for Φ13(X,Y) is:
[14,0] 1
[13,13] -1
[12,2] 13
[10,4] 52
[8,6] 78
[1,1] 64
which indicates the polynomial
X14 − X13Y13 + 13X12Y2
+ 52X10Y4 + 78X8Y6+ 78X6Y8
+ 52X4Y10 + 13X2Y12 + 64XY+Y14.
Note that the polynomials are symmetric in X and Y but the file only lists one of the symmetric terms.
Individual links for primes below 1000 are provided below (we omit 2 and 3 since divide the level of ƒ).
A single gzipped tar file containing all these files may be downloaded from here.
Individual gzipped files for primes from 1000 to 5000 can be obtained from the directory listing.
Φ5(X,Y)
Φ7(X,Y)
Φ11(X,Y)
Φ13(X,Y)
Φ17(X,Y)
Φ19(X,Y)
Φ23(X,Y)
Φ29(X,Y)
Φ31(X,Y)
Φ37(X,Y)
Φ41(X,Y)
Φ43(X,Y)
Φ47(X,Y)
Φ53(X,Y)
Φ59(X,Y)
Φ61(X,Y)
Φ67(X,Y)
Φ71(X,Y)
Φ73(X,Y)
Φ79(X,Y)
Φ83(X,Y)
Φ89(X,Y)
Φ97(X,Y)
Φ101(X,Y)
Φ103(X,Y)
Φ107(X,Y)
Φ109(X,Y)
Φ113(X,Y)
Φ127(X,Y)
Φ131(X,Y)
Φ137(X,Y)
Φ139(X,Y)
Φ149(X,Y)
Φ151(X,Y)
Φ157(X,Y)
Φ163(X,Y)
Φ167(X,Y)
Φ173(X,Y)
Φ179(X,Y)
Φ181(X,Y)
Φ191(X,Y)
Φ193(X,Y)
Φ197(X,Y)
Φ199(X,Y)
Φ211(X,Y)
Φ223(X,Y)
Φ227(X,Y)
Φ229(X,Y)
Φ233(X,Y)
Φ239(X,Y)
Φ241(X,Y)
Φ251(X,Y)
Φ257(X,Y)
Φ263(X,Y)
Φ269(X,Y)
Φ271(X,Y)
Φ277(X,Y)
Φ281(X,Y)
Φ283(X,Y)
Φ293(X,Y)
Φ307(X,Y)
Φ311(X,Y)
Φ313(X,Y)
Φ317(X,Y)
Φ331(X,Y)
Φ337(X,Y)
Φ347(X,Y)
Φ349(X,Y)
Φ353(X,Y)
Φ359(X,Y)
Φ367(X,Y)
Φ373(X,Y)
Φ379(X,Y)
Φ383(X,Y)
Φ389(X,Y)
Φ397(X,Y)
Φ401(X,Y)
Φ409(X,Y)
Φ419(X,Y)
Φ421(X,Y)
Φ431(X,Y)
Φ433(X,Y)
Φ439(X,Y)
Φ443(X,Y)
Φ449(X,Y)
Φ457(X,Y)
Φ461(X,Y)
Φ463(X,Y)
Φ467(X,Y)
Φ479(X,Y)
Φ487(X,Y)
Φ491(X,Y)
Φ499(X,Y)
Φ503(X,Y)
Φ509(X,Y)
Φ521(X,Y)
Φ523(X,Y)
Φ541(X,Y)
Φ547(X,Y)
Φ557(X,Y)
Φ563(X,Y)
Φ569(X,Y)
Φ571(X,Y)
Φ577(X,Y)
Φ587(X,Y)
Φ593(X,Y)
Φ599(X,Y)
Φ601(X,Y)
Φ607(X,Y)
Φ613(X,Y)
Φ617(X,Y)
Φ619(X,Y)
Φ631(X,Y)
Φ641(X,Y)
Φ643(X,Y)
Φ647(X,Y)
Φ653(X,Y)
Φ659(X,Y)
Φ661(X,Y)
Φ673(X,Y)
Φ677(X,Y)
Φ683(X,Y)
Φ691(X,Y)
Φ701(X,Y)
Φ709(X,Y)
Φ719(X,Y)
Φ727(X,Y)
Φ733(X,Y)
Φ739(X,Y)
Φ743(X,Y)
Φ751(X,Y)
Φ757(X,Y)
Φ761(X,Y)
Φ769(X,Y)
Φ773(X,Y)
Φ787(X,Y)
Φ797(X,Y)
Φ809(X,Y)
Φ811(X,Y)
Φ821(X,Y)
Φ823(X,Y)
Φ827(X,Y)
Φ829(X,Y)
Φ839(X,Y)
Φ853(X,Y)
Φ857(X,Y)
Φ859(X,Y)
Φ863(X,Y)
Φ877(X,Y)
Φ881(X,Y)
Φ883(X,Y)
Φ887(X,Y)
Φ907(X,Y)
Φ911(X,Y)
Φ919(X,Y)
Φ929(X,Y)
Φ937(X,Y)
Φ941(X,Y)
Φ947(X,Y)
Φ953(X,Y)
Φ967(X,Y)
Φ971(X,Y)
Φ977(X,Y)
Φ983(X,Y)
Φ991(X,Y)
Φ997(X,Y)