{
  "id": 2666,
  "curve_key": "403085445889:-217970029385027713",
  "ainvs": [
    "1",
    "0",
    "0",
    "-8397613456",
    "252279426801920"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 80.16724320287258,
  "faltings_height": 4.674247666838408,
  "conductor": "9682530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "37",
    "61"
  ],
  "discriminant": "10405980128230749229962263040000",
  "regulator": "14.6059507234668463041337710942619962027766",
  "points": [
    [
      "-89182",
      "17129516"
    ],
    [
      "-24832",
      "21119216"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=12; A=(3q-p)(p+q)^3=-134017, B=-(p+3q)(p-q)^3=557183. 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 20:16:45",
  "updated_at": "2026-09-26 20:16:45"
}