{
  "id": 2599,
  "curve_key": "725128613501769:-18268565814042151114053",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-15106846114620",
    "21144177172593648000"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.65211045895063,
  "faltings_height": 6.506252007987639,
  "conductor": "1376845470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
    "31"
  ],
  "discriminant": "27511846929025637252307955040804432547600",
  "regulator": "13.5107263935341041449296755804427100446677",
  "points": [
    [
      "1760148",
      "83032524"
    ],
    [
      "2725860",
      "466628880"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-60, q=31; A=(3q-p)(p+q)^3=-3731517, B=-(p+3q)(p-q)^3=24867843. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 20:11:53",
  "updated_at": "2026-09-26 20:11:53"
}