{
  "id": 2299,
  "curve_key": "76675419912529:-638039140505544019033",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1597404581511",
    "738471094319923785"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 95.91180690731561,
  "faltings_height": 5.931828776172332,
  "conductor": "4465059690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "47",
    "89"
  ],
  "discriminant": "25283594524148216618618663783732865600",
  "regulator": "4.682482476168032117824363843360286922081",
  "points": [
    [
      "2345439/4",
      "465385965/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=34; A=(3q-p)(p+q)^3=1065015, B=-(p+3q)(p-q)^3=9240247. 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 19:52:55",
  "updated_at": "2026-09-26 19:52:55"
}