{
  "id": 4551,
  "curve_key": "5824099689821376818401:-285703595331683566068305888187601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-121335410204612017050",
    "330675457549707658024969702500"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 150.34887414208148,
  "faltings_height": 10.565598784710751,
  "conductor": "488741877386656530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "43",
    "53",
    "79",
    "137",
    "977"
  ],
  "discriminant": "67087798693382267211783930683588706930065360186513817600000000",
  "regulator": "112126.86491097232856471918166312677948691957415517",
  "points": [
    [
      "-393368898",
      "615097070847402"
    ],
    [
      "31557891300",
      "5284878316545750"
    ],
    [
      "-109030713740/9",
      "4063483216812370/27"
    ],
    [
      "36645802260",
      "6715369459967190"
    ],
    [
      "168991360387980/17161",
      "677233435974631892850/2248091"
    ],
    [
      "906690977459124/25",
      "27301649383055672153022/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Independent bounded rational-parameter specialization search of the Dujella-Peral Z/2Z x Z/4Z family using the conic coordinates in Manvir Jaswal (2026), Section 7, Zenodo record 23437118. Parameter k = -1. Family attribution: Andrej Dujella and Juan Carlos Peral; conic parametrization attribution: Manvir Jaswal. No rank was inherited from the family.\r\n\r\nFresh PARI/GP 2.15.4 rank bounds [6,6]. Six 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: 7th of 45 by conductor. Literature-wide novelty remains open.",
  "created_at": "2026-10-17 22:46:44",
  "updated_at": "2026-10-17 22:46:44"
}