{
  "id": 2397,
  "curve_key": "8061150615961:-22879586136565908541",
  "ainvs": [
    "1",
    "0",
    "1",
    "-167940637833",
    "26480988477824056"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 89.15423225574322,
  "faltings_height": 5.16493498108954,
  "conductor": "133461510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "31",
    "83"
  ],
  "discriminant": "205689061592413864953327720562500",
  "regulator": "2.538463755144404751451446377267070943759",
  "points": [
    [
      "-300760",
      "223276167"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-26, q=19; A=(3q-p)(p+q)^3=-28469, B=-(p+3q)(p-q)^3=2824875. 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 19:59:03",
  "updated_at": "2026-09-26 19:59:03"
}