nr2 := array(symmetric,1 .. 8, 1 .. 8,[(6, 6)=1,(1, 5)=1,(4, 7)=-1,(1, 7)=1,(
3, 8)=1,(5, 8)=-1,(2, 8)=1,(7, 8)=-1,(5, 7)=1,(2, 4)=-1,(3, 3)=-1,(2, 5)=-1,(3
, 6)=-1,(1, 6)=1,(1, 3)=1,(4, 6)=1,(1, 2)=1,(6, 7)=1,(1, 1)=1,(4, 8)=1,(2, 7)=1
,(4, 4)=-1,(2, 3)=-1,(5, 5)=1,(7, 7)=-1,(8, 8)=-1,(3, 7)=-1,(2, 2)=1,(6, 8)=-1,
(2, 6)=-1,(3, 5)=1,(1, 8)=1,(1, 4)=1,(3, 4)=1,(5, 6)=-1,(4, 5)=-1]):
nrp := array(symmetric,1 .. 4, 1 .. 4,[(2, 4)=-1,(3, 3)=1,(1, 3)=1,(1, 2)=1,(1
, 1)=1,(4, 4)=1,(2, 3)=-1,(2, 2)=1,(1, 4)=1,(3, 4)=-1]):
nrq := array(symmetric,1 .. 4, 1 .. 4,[(2, 4)=1,(3, 3)=1,(1, 3)=1,(1, 2)=1,(1, 
1)=1,(4, 4)=-1,(2, 3)=-1,(2, 2)=-1,(1, 4)=1,(3, 4)=-1]):
alf := [A, B, C, D, E, F, G, H,I_, J, K, L, M, N, O, P, Q, R, S, T, U
, V, W, X, Y, Z]:ts1d:=50:
ts1 := 1.-.57721566490153286060651209008240243104215933593992*s+
.98905599532797255539539565150063470793918352072822*s**2-
.90747907608088628901656016735627511492861144907239*s**3+
.98172808683440018733638029402185085036057367972337*s**4-
.98199506890314520210470141379137467551742650714739*s**5+
.99314911462127619315386725332865849803749075523948*s**6-
.99600176044243153397007841966456668673529880955476*s**7+
.99810569378312892197857540308836723752396852479035*s**8-
.99902526762195486779467805964888808853230396352581*s**9+
.99951565607277744106705087759437019443450329799477*s**10-
.99975659750860128702584244914060923599695138562902*s**11+
.99987827131513327572617164259000321938762910895453*s**12-
.99993906420644431683585223136895513185794350282821*s**13+
.99996951776348210449861140509195350726552804248010*s**14-
.99998475269937704874370963172444753832608332577167*s**15+
.99999237447907321585539509450510782583381634469489*s**16-
.99999618658947331202896495779561431380201731243290*s**17+
.99999809308113089205186619151459489773169557198856*s**18-
.99999904646891115771748687947054372632469616324973*s**19+
.99999952321060573957523929299106456816809968908617*s**20+O(1)*s**21:
I_F := [1.958060320, 1.985813038, 2.007385038, 2.024810633, 2.039291674, 
2.051590472, 2.071528799, 2.087169944, 2.099897458, 2.110538234, 2.119621635, 
2.137608748, 2.151153754, 2.161873368, 2.170658434, 2.178046915, 2.184386129, 
2.189912050, 2.194791591, 2.199146733, 2.203069058, 2.206628906, 2.209881356, 
2.212870265, 2.215631068, 2.218192763, 2.220579352, 2.222810906, 2.224904360, 
2.226874124, 2.228732550, 2.230490297, 2.232156623, 2.233739614, 2.235246371, 
2.236683159, 2.238055531, 2.239368430, 2.240626274, 2.241833026, 2.242992251, 
2.244107170, 2.245180699, 2.246215487, 2.247213948, 2.248178285, 2.249110513, 
2.252553200, 2.255606634, 2.258342745, 2.260815812, 2.263067716, 2.265131386, 
2.267033140, 2.268794319, 2.270432443, 2.271962056, 2.273395357, 2.274742664, 
2.276012779, 2.277213264, 2.278350661, 2.279430662, 2.280458250, 2.281437807, 
2.282373209, 2.283267895, 2.284124935, 2.284947073, 2.285736776, 2.286496267, 
2.287227557, 2.287932470, 2.288612663, 2.289269649, 2.289904812, 2.290519417, 
2.291114629, 2.291691520, 2.292251076, 2.292794212, 2.293321773, 2.293834542, 
2.294333250, 2.294818572, 2.295291143, 2.295751550]:
froB0 := table([(5)=[-2, -3, -4, -1],(37)=[3, 8, -8, -4, 7, -2, 8, 0, -2, 6, -6
, 4, 4, -7, 2, 1, -10, -2, 5, 4, -2, 7, 3, -10, 5, 2, 3, 8, -6, -2, 6, 10, 11, 
2, -1, -9, -11],(53)=[-10, -8, -1, 9, -6, 2, 10, 6, -4, -4, -6, 6, -6, 6, -9, -
3, 10, 12, -3, 2, 3, 6, 11, -14, 2, -9, -8, -5, 2, -2, 1, 4, 7, -4, -10, 1, -12
, 9, -6, -6, -11, -6, -3, 12, 2, 0, -5, -9, 13, 0, -12, -4],(79)=[9, -16, -16, 
-4, 2, 1, -8, 3, -5, 12, -11, -9, -1, -6, 0, 5, 0, -12, 4, 10, 0, -8, -14, -14
, -2, -8, 10, 1, -4, 7, -16, -5, -6, -4, -11, 11, 10, 10, 11, -1, 3, -8, -4, -2
, -13, -12, 14, 8, 8, 4, -10, 3, -10, -13, 17, -10, 15, -12, 14, -10, 6, -1, 4
, 0, 8, -5, -6, 4, 0, -7, -1, 2, 16, -8, 4, -8, -8, 15, 17],(7)=[3, -4, -1, -2
, -2, 0, [-1, 5, 4, -4, -5, 1]],(23)=[2, -4, 0, -1, 4, 8, -9, -8, 7, -4, 5, -3
, 4, 6, -3, 1, -2, 6, 0, 6, 3, 6],(97)=[0, 4, 2, 7, 8, -2, 13, -10, 13, -2, -16
, -6, -11, 5, 2, -10, 7, -17, -18, 0, -8, -12, -4, 10, 11, 17, -12, -12, 7, 1, 
2, -5, -12, -6, -7, -2, 2, -16, -16, -14, 2, -6, -17, -10, 8, -10, 9, 2, -10, 6
, 12, -3, -8, 1, 15, -14, 19, 4, -14, 8, -2, -2, 6, -18, -2, 14, -3, 14, 10, 3
, 1, -8, -13, 10, -9, -14, 9, 6, -18, -10, 1, 13, 14, 2, -18, -8, 5, -5, 8, -7
, 1, 16, 2, 4, 7, -12, -19],(41)=[-7, -5, 0, 10, -6, -8, 11, -3, -2, -1, 2, 12
, 6, -7, 9, -9, 2, 4, 8, 2, -2, 6, -10, 3, 6, 5, 9, 0, 6, -10, -5, 0, -6, 8, -6
, -4, 3, -3, 2, 12],(67)=[5, 1, 12, -4, 15, 2, 7, 9, -12, 11, 7, -8, -2, 4, 9, 
-2, -14, -4, -11, 10, -13, -12, 8, 12, 3, -1, 14, -8, -2, -2, -8, 4, -4, -2, 4
, -2, 8, 14, -8, 3, 5, -4, -6, -4, 3, -5, -8, 13, -10, 7, -4, 6, 0, -7, -10, 8
, 4, 12, -3, -2, 10, -13, 5, 12, 16, 0, -5],(83)=[7, 12, -12, 4, 12, -3, 2, 4, 
14, -17, -12, 1, -5, -4, -9, 4, 0, 7, 6, 6, -13, -7, 9, -10, 5, -1, 6, 0, -9, 6
, -10, 18, -3, 9, -6, -15, 12, -8, -2, -14, 12, 12, 6, -16, -6, 15, -4, -9, -12
, 0, 8, -2, 12, -11, -9, 2, 4, -16, -14, 5, 6, -11, -1, 16, -6, 8, 0, 0, -12, -
16, -9, 3, 6, -4, -15, 4, -11, 4, -3, 4, -14, 8],(11)=[0, 4, -6, -3, -5, 1, 2, 
-4, -2, 3],(43)=[-3, 10, 5, -6, 5, 7, -4, 0, -4, -2, -6, -4, 2, -7, -2, 12, -11
, -1, 11, 4, 9, 12, -1, -8, 1, -10, -6, 4, 4, 8, -4, 1, 1, 8, 8, 8, 2, -4, 9, -
10, 0, 6, -8],(59)=[-10, -14, -11, -3, -10, -3, -4, 10, 3, -14, 11, -10, 6, 4, 
0, 2, 0, -3, -12, -12, -7, -9, -8, -9, -4, 3, 6, 0, -1, 6, 8, 5, 5, 8, 6, -15, 
-13, -4, -9, 12, -6, 12, 4, 12, -1, 5, 0, 0, 12, -6, -4, 7, -4, 6, -4, -8, -2, 
9],(13)=[-6, -1, 5, 2, 0, 2, 4, 3, 1, 4, -2, 6, [-5, -7, 7, -2, 5, 2, 2, 5, -2
, 7, -7, -5]],(29)=[5, 0, -4, -1, -6, -6, 4, -1, 8, -3, -5, -6, -9, 6, 2, -2, 4
, -2, 10, 6, -7, -3, 6, -9, 0, -3, -2, -8],(61)=[-6, 10, 10, -2, 5, 2, 1, -15, 
0, 8, -3, -8, 2, -10, -14, 7, -13, -2, 13, 10, -1, -10, 1, -3, 5, 10, -12, 8, 
11, -4, 2, -2, -6, 9, 10, -5, -6, -12, 5, 10, 0, 7, -4, 14, 11, 4, -7, -8, 14, 
0, 4, 8, -6, 7, 8, 2, -2, 6, 1, 6, 1],(71)=[-3, 3, 1, -6, 6, 6, -8, -6, 4, -9, 
8, -6, 3, 2, -12, 10, 0, -10, 12, 8, 12, -14, -12, 0, -12, -13, 7, 9, 5, -9, -2
, 4, 16, -3, 16, 11, 10, -2, -1, 0, 0, 12, 13, 7, -4, -14, -6, 0, -3, -4, -15, 
8, -5, 15, 2, 8, -12, 6, 6, 8, 1, 5, 10, 5, 8, 0, -15, 12, -9, 8],(31)=[9, 0, 2
, 0, 2, -7, 10, -3, -2, 1, -8, -5, 8, 2, 6, -6, -8, -4, -8, -5, 4, -10, 0, 1, -
7, -4, -3, -4, 4, 5, -4],(47)=[-3, 2, -9, 4, -3, -9, 3, 8, 0, 0, 12, 6, 1, 9, -
6, 8, 7, -2, 6, -2, 1, -2, 7, 6, 8, -8, 6, -12, 8, 12, -7, -10, -4, -8, 4, 0, 4
, 12, -13, 11, 6, 5, 3, 0, -3, -10],(73)=[-3, -4, 9, -8, 2, -16, -6, -9, 0, 2, 
1, -13, 11, 1, 16, 10, 7, 10, 4, 10, -2, 6, 14, -11, 2, -14, -6, 4, 8, -3, -5, 
4, 11, -10, 4, 4, 5, -2, -2, -1, -2, -4, 2, 2, 11, -15, -10, -13, 6, -10, 3, -6
, 10, -14, -14, 0, 11, 7, 4, 8, -7, -14, -12, -6, -9, 6, -1, -7, 8, -12, -14, -
6, -7],(89)=[6, -14, 9, 12, -9, 0, 0, 4, 6, -8, 14, 15, 0, 12, -5, -15, 10, 8, 
-15, -7, -6, 10, -2, 18, -16, 10, -3, 9, -2, 6, 4, -15, 15, 18, -1, -13, 16, -5
, -2, -12, 6, -14, 12, -6, -1, 10, -11, 11, 6, -6, 14, 0, 3, -6, -6, 2, 9, -3, 
6, -10, 2, 14, 10, -4, -12, 0, -2, 8, -1, -14, 13, 4, 9, -8, 16, 3, -3, -12, 18
, -6, -1, 7, -6, -7, -10, 17, -5, 6],(17)=[6, -3, 1, -4, 4, 6, 3, 0, 2, 6, 8, 7
, -3, -2, -5, -2],(19)=[2, 8, 7, -1, -4, 1, 0, 3, -4, 5, 6, 6, -2, -2, 4, -5, -
4, 0, 7]]):
vog := 0:
basp := 500:
stak := 1:
iee := 0:
stac := 0:
pcn := 0:
eP := 0.0000001:
tim := 0:
niv := 0:
iflag := 0:
sflag := 0:
ft1 := []:
ft2 := []:
ft := []:
trou := []:
cwlt := []:
rflag := 0:
ljay := [-32768, -121, -24729001, -297756989/2, -882216989/131072, -884736, -
9317, -162677523113838677, -884736000, -147197952000, -262537412640768000]:
lcyo := {3, 5, 6, 7, 8, 9, 10, 13, 14, 15, 21, 24, 25}:
rm24 := {0, 1, 4, 9, 12, 16}:
fr5 := (F**2+10*F+5)**3-((a1**2+4*a2)**2-24*a1*a3-48*a4)**3/(1/1728*((a1**2+4*
a2)**2-24*a1*a3-48*a4)**3-1/1728*(-(a1**2+4*a2)**3+36*(a1**2+4*a2)*(a1*a3+2*a4)
-216*a3**2-864*a6)**2)*F:
fr7 := (F**2+13*F+49)*(F**2+5*F+1)**3-((a1**2+4*a2)**2-24*a1*a3-48*a4)**3/(1/
1728*((a1**2+4*a2)**2-24*a1*a3-48*a4)**3-1/1728*(-(a1**2+4*a2)**3+36*(a1**2+4*
a2)*(a1*a3+2*a4)-216*a3**2-864*a6)**2)*F:
fr13 := (F**2+5*F+13)*(F**4+7*F**3+20*F**2+19*F+1)**3-((a1**2+4*a2)**2-24*a1*a3
-48*a4)**3/(1/1728*((a1**2+4*a2)**2-24*a1*a3-48*a4)**3-1/1728*(-(a1**2+4*a2)**3
+36*(a1**2+4*a2)*(a1*a3+2*a4)-216*a3**2-864*a6)**2)*F:
lC := [7, 43, -7166093, -3897085, 472119155, 1, -2585, 257370410321695, 210, 
11935, 1239292670]:
CMj := [1728, 8000, 0, -3375, -32768, -884736, -884736000, -147197952000, -
262537412640768000, 287496, 54000, 16581375, -12288000]:
CMd := [-4, -8, -3, -7, -11, -19, -43, -67, -163, -16, -12, -28, -27]:
dI := [11, 11, 11, 17, 17, 19, 37, 37, 43, 67, 163]:
nC4 := [352, 174361, 121, 9162745, 145945, 1824, 9987985, 385, 41280, 353760, 
104372160]:
nC6 := [-6776, -72809693, 5203, 31092780275, -55755325, -77976, 31565801575, -
8225, -8387064, -210408408, -1066294102104]:
qD := ` not yet determined - use the command`:
cus := `present curve is `:
QT := `trouble in`:
QS := ` assuming B-SwD, the order of the Shafarevich-Tate group is `:
qtr := ` --- procedure aborted`:
qts := `improper args --- procedure aborted`:
qtt := `Curve is singular (DD=0) --- procedure aborted`: 
noc := ` not on cur`:
pno := `point not on cur`:
isog2 := `To save them for future apecs sessions either Ypecs(); now or`:
isog3 := `use the Zpecs(); command when you leave apecs.`:
PP:=NULL:NN:=-1:
RR:=[]:MM:=0:
QQ:=[]:
uR:={}:
sT:=-1:
p_up_to_100 := [2,3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 
61, 67, 71, 73, 79, 83, 89, 97, 101]:
MINK:=[1,4/3,2,4,8,64/3,64,256]:
quarm_flag:=false:
bec:=[]:bec_:=[]:bic:=[]:bic_:=[]:
bouu:=false:bouv:=true:
afacnops:=0:afacprimes:={}:afacflag:=true:afac(2):
p_at_inf_c:=[]:at_inf_c:=[]:p_at_inf_w:=[]:at_inf_w:=[]: