{
  "id": 2508,
  "curve_key": "4551259969:142415847913247",
  "ainvs": [
    "1",
    "0",
    "0",
    "-94817916",
    "-164841058800"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 66.71600984351632,
  "faltings_height": 3.61332954814136,
  "conductor": "1111110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "37"
  ],
  "discriminant": "42819662302946934947942400",
  "regulator": "2.733043379245865586479501181347058123854",
  "points": [
    [
      "-8400",
      "201540"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=12; A=(3q-p)(p+q)^3=49247, B=-(p+3q)(p-q)^3=76895. 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 20:05:57",
  "updated_at": "2026-09-26 20:05:57"
}