{
  "id": 2236,
  "curve_key": "815105311296409:-11715891289695401325373",
  "ainvs": [
    "1",
    "0",
    "1",
    "-16981360652009",
    "13560057947959993496"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 103.00301531140894,
  "faltings_height": 6.634268629165384,
  "conductor": "29730862590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "41",
    "61",
    "163"
  ],
  "discriminant": "233964782750564963318137716355690090628100",
  "regulator": "5.126823677285206335833736378353686776171",
  "points": [
    [
      "3749873",
      "1614025128"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=51; A=(3q-p)(p+q)^3=11234123, B=-(p+3q)(p-q)^3=32458283. 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 19:48:55",
  "updated_at": "2026-09-26 19:48:55"
}