use strict;
use warnings;
use strict;

while (<DATA>)
{
   if (/^Curve(\d):/.../^\s*$/)
   {
     if (defined($1) && $1==1 && /^\d/) {print "C1: $_\n";};
     if (defined($1) && $1==2 && /^\d/) {print "C2: $_\n"};
   }
}

__DATA__
Curve1:
123, 456
   end 123

Curve2:
789, 101
   end 123
[download]

Prints:

C1: 123, 456

C2: 789, 101
[download]

Using $1 etc after a failed match is generally an error, but not in this case. The fact that $1 is not reset is relied on by the code.