{
  "id": 2445,
  "curve_key": "1481734343761:-1803375364010241241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-30869465495",
    "2087237432186025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.07270311453692,
  "faltings_height": 4.7165807000076665,
  "conductor": "33211230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "31",
    "41",
    "67"
  ],
  "discriminant": "601491151850980798856241000000",
  "regulator": "5.636252846937419915176159743307006011938",
  "points": [
    [
      "-189050",
      "34248445"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=18; A=(3q-p)(p+q)^3=8375, B=-(p+3q)(p-q)^3=1221431. 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 20:02:02",
  "updated_at": "2026-09-26 20:02:02"
}