{
  "id": 2306,
  "curve_key": "55917128146609:-292592047035927060073",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1164940169721",
    "338648105509531065"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 94.96467556821801,
  "faltings_height": 5.942162699508618,
  "conductor": "64127910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "71"
  ],
  "discriminant": "51636220385698395361387621800205646400",
  "regulator": "2.962269791837816652702122570343690638614",
  "points": [
    [
      "-1173912",
      "297998301"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=22; A=(3q-p)(p+q)^3=-2263545, B=-(p+3q)(p-q)^3=6084487. 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 19:53:23",
  "updated_at": "2026-09-26 19:53:23"
}