I have fought water issues in my property for years. I currently send my basement sump about 80 feet to a storm sewer in the street. It travels through the typical sump output PVC that is 1.5" and meets a 3" drain thin wall drain line after about 25' and a few bends (3 90s and a 45). Never had a problem with this setup. Remember, LEVEL is no good in Indianapolis. it has to maintain a constant downward slope and completely empty each time you pump water . See freezing below !!!
I think so long as you follow some common sense about having a good downward slope on the length of pipe the limiting factor is more the height that you expect the water to rise, which is probably "not much". I suspect that you would go up at most 8' from your basement floor and then go back to ground level and down from there. Even though I go to a larger pipe, I bet the 1.5 for the entire distance would be fine. On my 3" pipe I used the solid thin wall pipe buried not too far underground... several inches of soil above at most.
Things to consider:
1. Freezing. Its a concern. If you don't have positive drainage and have any standing water above the freeze line, it will freeze solid and then you are done. Might want to include a "blow out" fitting just outside your house so that you pump onto your lawn if your buried line gets obstructed.
Your line might also freeze if it sinks over time and fills with water. It was common around here to pump water through a pipe that goes through the curb and dumps onto the street. I have heard of leaves creating a pool of water at the outlet of a pipe like that and freezing. Moral there is you have to maintain even what you think is installed correctly.
2. Damage: I know where I have buried lines/pipes. I would never consider letting anything of significant weight drive over those pipes.... lawn tractor OK, cement truck NO. If you have flexibility on your placement, keep that in mind
Finally, protect that patio. that looks like a very nice stamped patio and your sump pump will be removing more and more of its foundation. I would move that drain ASAP and see what can be done about supporting the patio once it dries. Not sure what to suggest, but you want to keep it supported and discourage wildlife from moving into already hollowed out areas.