{
  "id": 2415,
  "curve_key": "2069369993161:-2852456323451438341",
  "ainvs": [
    "1",
    "0",
    "1",
    "-43111874858",
    "3301450485412556"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 85.07479597725501,
  "faltings_height": 5.0203453013286055,
  "conductor": "145680990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "43",
    "73"
  ],
  "discriminant": "419641110208951190337947510250000",
  "regulator": "4.945438934105033578066365231192149332181",
  "points": [
    [
      "77157",
      "20803693"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=15; A=(3q-p)(p+q)^3=-160381, B=-(p+3q)(p-q)^3=1351619. 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 20:00:11",
  "updated_at": "2026-09-26 20:00:11"
}