{
  "id": 2613,
  "curve_key": "3122914120122241:-174517929472090067760961",
  "ainvs": [
    "1",
    "0",
    "0",
    "-65060710835880",
    "201988338874674638400"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 107.03262892101952,
  "faltings_height": 6.404705922599728,
  "conductor": "3621047430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "41",
    "173"
  ],
  "discriminant": "831189112439739863769076493376000000",
  "regulator": "15.6964662779841475666898583667830582996346",
  "points": [
    [
      "4654686",
      "5731422"
    ],
    [
      "18688143/4",
      "433213461/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=44; A=(3q-p)(p+q)^3=4671, B=-(p+3q)(p-q)^3=55885375. 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 20:12:46",
  "updated_at": "2026-09-26 20:12:46"
}