{
  "id": 2650,
  "curve_key": "1077477295129:251713042566289667",
  "ainvs": [
    "1",
    "0",
    "1",
    "-22447443649",
    "-291336410627584"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 83.1169307606888,
  "faltings_height": 4.99150018626807,
  "conductor": "159232710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "47",
    "73"
  ],
  "discriminant": "687237094185179431761666867896100",
  "regulator": "22.2049297395412339579585304696165352520393",
  "points": [
    [
      "-120887",
      "25666478"
    ],
    [
      "-69416",
      "30569768"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=13; A=(3q-p)(p+q)^3=-676053, B=-(p+3q)(p-q)^3=519115. 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 20:15:30",
  "updated_at": "2026-09-26 20:15:30"
}