First, a couple of NFL Draft Trade Value Charts
Classic Jimmy Johnson Model:
Rich Hill Modern Valuation Model:
Fitzgerald-Spielberger NFL Draft Trade Value Model:
NFL Draft Trade Value Chart | Over the Cap
overthecap.com
Trading with the Giants, the Patriots would receive their 1st (6th overall) and 2nd (39th) on the first model; on the second two the Pats probably would also need to give NYG their 3rd.
Trading with the Falcons, the Patriots would receive 1.8, 2.43 and 3.74 according to the original JJ model. On the Rich Hill model it would be the Pats sending 1.3 and 4.104 to Atlanta, and receive 1.8 and 2.43. According to the last model it would be Atlanta sending NE their 1.8 and 2.43, then the Pats giving up a bit more - maybe exchanging each other's 3rds and 4ths.
A trade with Minnesota might get a little trickier, since the Vikings don't have a 3rd. But on the last two models it would be the Pats receiving 1.11 and 2.42; one model has the Pats also receiving a 5th while the other is the oppossite, the Patriots also sending their own 5th to Minnesota.