Between the 2007 and 2010 seasons, the New England Patriots scored the most rushing touchdowns by a team, with 76 touchdowns.

which team leads the league in rushing touchdowns from 2007 to 2010
PatriotsTitansVikingsJaguarsChargersGiantsSaintsRavensDolphinsPanthersColtsJetsTexansEaglesFalconsPackersSteelersCowboys767372686765646462626161615959555050
TEAMGPRUSH TDRUSH YDSATTRUSH AVGRUSH YDS/G
New England PatriotsNew England Patriots64768,0211,8844.3125.3
Tennessee TitansTennessee Titans64738,6271,9564.4134.8
Minnesota VikingsMinnesota Vikings64728,8321,9214.6138.0
Jacksonville JaguarsJacksonville Jaguars64688,5891,9074.5134.2
San Diego ChargersSan Diego Chargers64676,9981,7903.9109.3
New York GiantsNew York Giants64658,7031,8944.6136.0
New Orleans SaintsNew Orleans Saints64646,6851,6384.1104.5
Baltimore RavensBaltimore Ravens64648,2041,9934.1128.2
Miami DolphinsMiami Dolphins64627,3401,7914.1114.7
Carolina PanthersCarolina Panthers64628,6051,9084.5134.5
Indianapolis ColtsIndianapolis Colts64615,7571,5753.790.0
New York JetsNew York Jets64618,8352,0094.4138.0
Houston TexansHouston Texans64616,9491,6974.1108.6
Philadelphia EaglesPhiladelphia Eagles64597,6321,6604.6119.3
Atlanta FalconsAtlanta Falcons64597,7301,8934.1120.8
Green Bay PackersGreen Bay Packers64556,8931,6844.1107.7
Pittsburgh SteelersPittsburgh Steelers64507,5751,8704.1118.4
Dallas CowboysDallas Cowboys64507,3581,6844.4115.0
Arizona CardinalsArizona Cardinals64485,5001,4273.985.9
Denver BroncosDenver Broncos64477,1991,6544.4112.5
Oakland RaidersOakland Raiders64468,2681,8814.4129.2
Washington RedskinsWashington Redskins64446,9371,7184.0108.4
Detroit LionsDetroit Lions64435,8491,4893.991.4
Cleveland BrownsCleveland Browns64427,2331,7604.1113.0
Tampa Bay BuccaneersTampa Bay Buccaneers64427,3371,7354.2114.6
San Francisco 49ersSan Francisco 49ers64406,3331,5264.299.0
Chicago BearsChicago Bears64396,1111,6443.795.5
Seattle SeahawksSeattle Seahawks64396,3771,6273.999.6
Buffalo BillsBuffalo Bills64367,2291,7124.2113.0
Kansas City ChiefsKansas City Chiefs64367,6141,7564.3119.0
Cincinnati BengalsCincinnati Bengals64336,6541,7693.8104.0
St. Louis RamsSt. Louis Rams64266,5381,6613.9102.2
StatMuse has team, season-level data for rushing touchdowns going back to the 1921 season.

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