{
  "id": 2718,
  "curve_key": "4034629086399289:-256105004708907593541613",
  "ainvs": [
    "1",
    "0",
    "1",
    "-84054772633319",
    "296417822519634217526"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 107.80107230502813,
  "faltings_height": 6.741974738687166,
  "conductor": "15695192370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "29",
    "41",
    "181"
  ],
  "discriminant": "50262916667561959636666584835674681320100",
  "regulator": "60.074076197109682290701246444236650133404472",
  "points": [
    [
      "-10555911",
      "2739567832"
    ],
    [
      "5446020",
      "419287837"
    ],
    [
      "5487963",
      "640201618"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=41; A=(3q-p)(p+q)^3=-889253, B=-(p+3q)(p-q)^3=63069435. 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 20:19:10",
  "updated_at": "2026-09-26 20:19:10"
}