{
  "id": 2505,
  "curve_key": "6069342409:-288866431050373",
  "ainvs": [
    "1",
    "0",
    "1",
    "-126444634",
    "334325609996"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 67.57954830465847,
  "faltings_height": 3.672002338018315,
  "conductor": "178710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "37"
  ],
  "discriminant": "81094935915800986742841600",
  "regulator": "5.304874192082891415495876555442050333670",
  "points": [
    [
      "1165",
      "433697"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=7; A=(3q-p)(p+q)^3=-26973, B=-(p+3q)(p-q)^3=60835. 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 20:05:46",
  "updated_at": "2026-09-26 20:05:46"
}