{
  "id": 2479,
  "curve_key": "727255376929:-620190263904653233",
  "ainvs": [
    "1",
    "0",
    "0",
    "-15151153686",
    "717811542849060"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 81.93763058340843,
  "faltings_height": 4.4627816590160565,
  "conductor": "4829370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "29",
    "61"
  ],
  "discriminant": "5604254832567097086286233600",
  "regulator": "5.969763613136581258363480120736758757957",
  "points": [
    [
      "59766",
      "5046654"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=16; A=(3q-p)(p+q)^3=1647, B=-(p+3q)(p-q)^3=853615. 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 20:04:10",
  "updated_at": "2026-09-26 20:04:10"
}