{
  "id": 2594,
  "curve_key": "1029737808620929:-32820779901356258720833",
  "ainvs": [
    "1",
    "0",
    "0",
    "-21452871012936",
    "37987011986978640960"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 103.70424183003213,
  "faltings_height": 6.490368299268951,
  "conductor": "12028260090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "31",
    "67",
    "109"
  ],
  "discriminant": "8500661207454932455254217640906866790400",
  "regulator": "22.1474157701972158190154610036638978561521",
  "points": [
    [
      "2484576",
      "151419624"
    ],
    [
      "9965439/4",
      "479850657/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=44; A=(3q-p)(p+q)^3=1435455, B=-(p+3q)(p-q)^3=32783167. 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 20:11:34",
  "updated_at": "2026-09-26 20:11:34"
}