180603

PARI


Hilbert class polynomial

D = -3, -4, -7, -8, ... , -23, -24 の場合について出力してみた。

(18:55) gp > a = ellj((1+sqrt(3)*I)/2)
%1 = -4.158163906257959687 E-112
(18:56) gp > Vecrev(polclass(-3))
%2 = [0, 1]
(18:56) gp > a = ellj(I)
%3 = 1728.0000000000000000000000000000000000
(18:56) gp > Vecrev(polclass(-4))
%4 = [-1728, 1]
(18:56) gp > a = ellj((1+sqrt(7)*I)/2)
%5 = -3374.9999999999999999999999999999999999
(18:56) gp > Vecrev(polclass(-7))
%6 = [3375, 1]
(18:56) gp > a = ellj(sqrt(2)*I)
%7 = 7999.9999999999999999999999999999999996
(18:56) gp > Vecrev(polclass(-8))
%8 = [-8000, 1]
(18:56) gp > a = ellj((1+sqrt(11)*I)/2)
%9 = -32768.000000000000000000000000000000001
(18:57) gp > Vecrev(polclass(-11))
%10 = [32768, 1]
(18:57) gp > a = ellj(sqrt(3)*I)
%11 = 54000.000000000000000000000000000000001
(18:57) gp > Vecrev(polclass(-12))
%12 = [-54000, 1]
(18:57) gp > a = ellj((1+sqrt(15)*I)/2)
%13 = -191657.83286254720747135344482127304994
(18:57) gp > b = ellj((1+sqrt(15)*I)/4)
%14 = 632.83286254720747135344482127304993337 - 5.798437327009191225 E-36*I
(18:57) gp > a*b
%15 = -121287375.00000000000000000000000000000 + 1.1113159320838825583 E-30*I
(18:57) gp > a+b
%16 = -191025.00000000000000000000000000000000 - 5.798437327009191225 E-36*I
(18:57) gp > Vecrev(polclass(-15))
%17 = [-121287375, 191025, 1]
(18:58) gp > a = ellj(2*I)
%18 = 287496.00000000000000000000000000000000
(18:58) gp > Vecrev(polclass(-16))
%19 = [-287496, 1]
(18:58) gp > a = ellj((1+sqrt(19)*I)/2)
%20 = -884736.00000000000000000000000000000002
(18:58) gp > Vecrev(polclass(-19))
%21 = [884736, 1]
(18:58) gp > a = ellj(sqrt(5)*I)
%22 = 1264538.9094751405093202270474107034214
(18:58) gp > b = ellj((1+sqrt(5)*I)/2)
%23 = -538.90947514050932022704741070342148143
(18:58) gp > a*b
%24 = -681471999.99999999999999999999999999997
(18:58) gp > a+b
%25 = 1264000.0000000000000000000000000000000
(18:58) gp > Vecrev(polclass(-20))
%26 = [-681472000, -1264000, 1]
(18:58) gp > a = ellj((1+sqrt(23)*I)/2)
%27 = -3493225.6999699333682055047385473297032
(18:59) gp > b = ellj((1+sqrt(23)*I)/4)
%28 = 737.84998496668410275236927366485169810 - 1764.0189386127461416437864271809651160*I
(18:59) gp > c = ellj((-1+sqrt(23)*I)/4)
%29 = 737.84998496668410275236927366485169810 + 1764.0189386127461416437864271809651160*I
(18:59) gp > a*b*c
%30 = -12771880859374.999999999999999999999999 + 0.E-25*I
(18:59) gp > a*b+b*c+c*a
%31 = -5151296874.9999999999999999999999999998 + 0.E-28*I
(18:59) gp > a+b+c
%32 = -3491749.9999999999999999999999999999999 + 0.E-35*I
(18:59) gp > Vecrev(polclass(-23))
%33 = [12771880859375, -5151296875, 3491750, 1]
(18:59) gp > a = ellj(sqrt(6)*I)
%34 = 4831907.9033513397453973662980491459803
(18:59) gp > b = ellj(sqrt(6)*I/2)
%35 = 3036.0966486602546026337019508540195888
(18:59) gp > a*b
%36 = 14670139391.999999999999999999999999999
(19:00) gp > a+b
%37 = 4834943.9999999999999999999999999999999
(19:00) gp > Vecrev(polclass(-24))
%38 = [14670139392, -4834944, 1]
(19:00) gp >