{
  "id": 4550,
  "curve_key": "11350504951329418428801:-1209599471023603978307000326683201",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-236468853152696217267",
    "1399999387817918114106461469459"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    7
  ],
  "family": null,
  "families": [],
  "naive_height": 152.3511947158628,
  "faltings_height": 10.424095683730856,
  "conductor": "689585803575130",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "43",
    "79",
    "3779",
    "69763"
  ],
  "discriminant": "-463165127676081192283014719291202123593980430054850560000000",
  "regulator": "1844.742174502489533361601059984037312637001252",
  "points": [
    [
      "27230960827",
      "3892693634521506"
    ],
    [
      "9467524689",
      "99176993641568"
    ],
    [
      "6444935867",
      "379044761308066"
    ],
    [
      "2885157584234723/344569",
      "16977719973528116595398/202262003"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Independent bounded rational-parameter specialization search of the Z/7Z family in Kulesz (2003), Theorem 2.6, with t = -2(u-3)/(u^2+3) and parameter u = 19/8. Family attribution: Leopoldo Kulesz.\r\n\r\nFresh PARI/GP 2.15.4 rank bounds [4,4]. Four rational points are supplied and passed a local replay of the ICARM exact mod-2 independence certificate. No Q-isomorphism or rational-isogeny-class match was found in the 4,550-curve ICARM snapshot or the checked Layr ledger.\r\n\r\nProjected within the matching torsion and rank pool: 6th of 23 by absolute minimal discriminant and 7th of 23 by conductor, Faltings height, and naive height. Literature-wide novelty remains open.",
  "created_at": "2026-10-17 22:44:50",
  "updated_at": "2026-10-17 22:44:50"
}