SELECT 
  cscart_product_point_prices.product_id, 
  MIN(
    cscart_product_point_prices.point_price
  ) AS point_price 
FROM 
  cscart_product_point_prices 
WHERE 
  cscart_product_point_prices.product_id IN (
    10370, 10372, 10374, 10376, 10377, 10378, 
    10379, 10380, 10381, 10371, 10373, 
    10375, 12944, 15781, 12853, 12854, 
    12855, 12856, 12551
  ) 
  AND cscart_product_point_prices.lower_limit = 1 
  AND cscart_product_point_prices.usergroup_id IN (0, 0, 1)

Query time 0.00030

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_product_point_prices",
      "access_type": "ref",
      "possible_keys": ["unique_key", "src_k"],
      "key": "unique_key",
      "key_length": "2",
      "used_key_parts": ["lower_limit"],
      "ref": ["const"],
      "rows": 1,
      "filtered": 100,
      "index_condition": "cscart_product_point_prices.product_id in (10370,10372,10374,10376,10377,10378,10379,10380,10381,10371,10373,10375,12944,15781,12853,12854,12855,12856,12551) and cscart_product_point_prices.usergroup_id in (0,0,1)"
    }
  }
}