{
  "id": 2611,
  "curve_key": "141345011743321:-1679424612398012860381",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2944687744653",
    "1943778241181128756"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 97.74667472801416,
  "faltings_height": 5.9006026106864615,
  "conductor": "417086670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "43"
  ],
  "discriminant": "1957117331642647582518434847585562500",
  "regulator": "8.97260985204571808416584122286684662234423",
  "points": [
    [
      "924077",
      "107919234"
    ],
    [
      "1021130",
      "39593922"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=27; A=(3q-p)(p+q)^3=-158389, B=-(p+3q)(p-q)^3=11808875. 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 20:12:38",
  "updated_at": "2026-09-26 20:12:38"
}