{
  "id": 2589,
  "curve_key": "10707643819745761:-1094479267312867249884241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-223075912911370",
    "1266758392652085092900"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 110.72920277103262,
  "faltings_height": 7.1013411535627755,
  "conductor": "75752014470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "29",
    "31",
    "89",
    "151"
  ],
  "discriminant": "17236939916172781832918641552507185216000000",
  "regulator": "30.8141312198930208323799375499320982991320",
  "points": [
    [
      "9418976",
      "1107074822"
    ],
    [
      "9550120",
      "2710622950"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=60; A=(3q-p)(p+q)^3=6226319, B=-(p+3q)(p-q)^3=106450319. 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 20:11:15",
  "updated_at": "2026-09-26 20:11:15"
}