{
  "id": 2192,
  "curve_key": "12121217819622081:-1334118175292224976383521",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-252525371242127",
    "1544118321571418014679"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 111.1012015520127,
  "faltings_height": 6.9883208460563555,
  "conductor": "2616270930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "43"
  ],
  "discriminant": "593488963998184413714867761433513984000000",
  "regulator": "2.500142081683455469821696572868383774055",
  "points": [
    [
      "9033759",
      "310382698"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=56; A=(3q-p)(p+q)^3=1016991, B=-(p+3q)(p-q)^3=110601375. 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 19:46:09",
  "updated_at": "2026-09-26 19:46:09"
}