{
  "id": 2598,
  "curve_key": "6807601583238289:-561681696569871860717113",
  "ainvs": [
    "1",
    "0",
    "0",
    "-141825032984131",
    "650094544396376719745"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 109.37044878785481,
  "faltings_height": 6.701869537340665,
  "conductor": "9143194830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "53",
    "191"
  ],
  "discriminant": "776967267310278346839009104500882305600",
  "regulator": "18.6909636372170450131261202625976494117269",
  "points": [
    [
      "6831706",
      "192601969"
    ],
    [
      "6899648",
      "98909951"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=46; A=(3q-p)(p+q)^3=-65513, B=-(p+3q)(p-q)^3=82475415. 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 20:11:49",
  "updated_at": "2026-09-26 20:11:49"
}