{
  "id": 2604,
  "curve_key": "711392020019209:-18970847585392585254373",
  "ainvs": [
    "1",
    "0",
    "1",
    "-14820667083734",
    "21956998285074716696"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.59473427426708,
  "faltings_height": 6.263344311011587,
  "conductor": "5192997810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "67",
    "89"
  ],
  "discriminant": "73624888444392981043347313263293744400",
  "regulator": "24.2755182125999965434104675884723874329066",
  "points": [
    [
      "8532711/4",
      "1758636689/8"
    ],
    [
      "2179353",
      "91346953"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=39; A=(3q-p)(p+q)^3=192995, B=-(p+3q)(p-q)^3=26767907. 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 20:12:12",
  "updated_at": "2026-09-26 20:12:12"
}