###########################
# datF for Apecs5
###########################

lprint(`Reading Dat/dat ..`);

Dat:=proc() 
global  e21, e24, iee, k, ncir, p, s;
local a,d,i,j,l,n,x,y;
#Display data of any curve in the stack or catalog
  l:=proc() lprint(args):end:
  if nargs=0 then
    if cur='cur' then 
      if sT=4 then print(`Curve is singular.`);fi;
      iee:=1:ill();iee:=0:l(`Present Weierstrass coeff.'s: `,yo):RETURN();
    fi;
    d:=[cur,ncur,Ncl,[Kod],NN,[PP],qR,RR,rc,r4,r1,dill,nisog,disog,visog,reg,o\
megA,shaf,SFE,tuQ,sB,tW,cP]:
    ncir:=ncur:
  else
    if ian(args)=2 then RETURN();fi;
    d:=[et1[ncir],ncir,op(eT[ncir])]:
  fi;
  print(`[a1..a6] = `,et2[ncir]);
  for k to 23 do e.k:=d[k]:od;
  l(`catalog name and number are: `.e1,e2);
  if ncir=ncur then iee:=1:ill();iee:=0:fi;
  if type(e3,list) then l(`conductor = `,e3[1],` = `,e3[2],`^`,e3[3]);
  else l(`conductor = `,e3,` = `,ifactor(e3));
  fi;
  l(`Kodaira type(s): `,op(e4),`; cP = `.e23);
  if e9=-1 then l(`rank`.qD,` Rk, Rk0, Rk1, RkNC or Crem`);
  else l(`rank = `.e10.`, determined as follows:`);
    if e9=0 then 
      l(`   from rank of an isogenous curve using the T, B-SD and R.H.c\
onjectures`);
    elif e9=1 then
      l(`   from the rank of an isogenous curve using only the T-p conject\
ure`);
    elif e9=2 then l(`   using the T, B-SD and R.H. conjectures`);
    elif e9=3 then l(`using only the T-p conjecture`);
    elif e9=4 then 
      l(`   from the rank of an isogenous curve using none of the stand\
ard conjectures`);
    elif e9=5 then l(`   directly using none of the standard conjectures\
`);
    else
      if e9=6 then l(`   for an isogenous curve,`);fi;
      l(e11,` was an upper bound for the rank`);
      if e11>1 then
        l(`   and that many independent points were found.`);
      elif e11=1 then
        l(`   and a point of infinite order was found.`);
      fi;
      l(`   thus confirming the value of the rank.`);
    fi;
  fi;
  if nops(e8)>0 then
    if e7<2 then
      l(`points of infinite order noticed: `,op(e8));
    elif e7=2 then
      l(`we only have the following independent points of infinite ord\
er: `,op(e8));
      l(`--- need`,r4);
    elif e7=9/4 then
      l(`Sha has determined that the present RR+torsion generates`);
      l(`a subgroup of finite index > 1.`);
    elif e7=5/2 then
      l(`we have the right number of independent point(s): RR =`);
      print(e8);
      l(`but they don't form a Mordell-Weil basis since yR is not empty\
.`);
      l(`yR contains points rationally but not integrally depenedent o\
n RR.)`);
    elif e7=3 then 
      l();
      l(`possible basis (right number and linearly independent), RR =`);
      l(e8);l(`grammian = `,evalf(e16));
    elif e7=4 then
      l();
      l(`probable basis --- RR consists of the succesive minima:`);
      l(e8);l(`discriminant (probably the regulator) = `,evalf(e16));
    else
      l();
      l(`"certified" basis: `,e8);l(`regulator = `,e16);
    fi;
  fi;
  if type(e21,list) then e21:=abs(e21[1]);else e21:=abs(e21);fi;
  if e7<2 and e21>1 then
    l(`searched for [x,y] on the curve with x=a/b^2 for max{|a|,b^2}<=`.e21);
  fi;
  if abs(e19)=1 then 
    l(`The sign of the functional equation is `,e19);
  fi;
  if e12>3 then 
    l(`searched for points on principal homogeneous spaces up to`);
    l(`   (naive) height = log `.e12);
  fi;
  isug(e13,e14);e24:=nops(e22[1]):
  if e24>0 then
    print(`   twist by|gives curve`);
    for i to e24 do print(cat(e22[1][i],`|`,et1[e22[2][i]]));od;
  fi;
  for i to nops(e17) do
    x:=e17[i]:
    if nops(x)<4 then 
       if ncir=ncur then Om();
       else 
         ein(ncir);Om();
         if type(psn,posint) then go(psn);fi;
       fi;
    else
      p:=x[1]:l(cat(p,`-adic period to `,x[2],` digits is`));y:=x[3]:
      s:=cat(p,`^`,y[1],`*`):print(s,y[2..nops(y)]);y:=x[4]:
      s:=cat(`with corresponding derivative^2 = `,p,`^`,y[1],`*`);
      print(s,y[2..nops(y)]);
    fi;
  od;
  if e18>0 then
    print(`shaf = conjectural order of Shafarevich-Tate group = `,e18);
  fi;
end:

dat:=proc() local b,x,q;
#Display catalog entry.
  q:=`,Kod,NN,PP,qR,RR,rc,r4,r1,dill,nisog,disog,visog,reg,omegA,shaf,\
SFE,tuQ,sB,tW,cP,misc:`:
  if nargs=0 then
    if cur='cur' then aM();RETURN();fi;
    print(cat('Ncl',q));print(`eT[`.ncur.`] = `.Ncl,[Kod],NN,[PP],qR,RR,rc,r4,\
r1,dill,nisog,disog,visog,reg,omegA,shaf,SFE,tuQ,sB,tW,cP,op(misc));
  else
    b:=args:
    if ian(b)=2 then RETURN();fi;
    x:=eT[ncir]:
    if type(x[1],list) then q:=cat('Ncl',q):
    else q:=cat('Nc',q):
    fi;    
    print(q);print(`eT[`.ncir.`] = `,x);
    if type(b,list) or type(b,integer) then
      print(`catalog name of curve is `,et1[ncir]);
    fi;
  fi;
end: