{
  "id": 4552,
  "curve_key": "42132482384506218971841:-9279550711887086977307665924643361",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-877760049677212895247",
    "10740220731570235125043916562519"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    7
  ],
  "family": null,
  "families": [],
  "naive_height": 156.4262423995245,
  "faltings_height": 10.98921537049718,
  "conductor": "10419596852100590",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "17",
    "23",
    "61",
    "337",
    "503",
    "3347"
  ],
  "discriminant": "-6550203015650467848448751003911537154195749153095000227840000000",
  "regulator": "12034.26766516133532702452767207126896409409119",
  "points": [
    [
      "-351741595900223/10201",
      "104102244454937324186/1030301"
    ],
    [
      "1818582379227",
      "2452121895534458886"
    ],
    [
      "36358958263267/1521",
      "109660132931913718634/59319"
    ],
    [
      "-1130317818720023821413/36995060281",
      "21391215617653154865484509851406/7115666889507821"
    ]
  ],
  "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 = 9/20. 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: 7th of 23 by absolute minimal discriminant, Faltings height, and naive height; 8th of 23 by conductor. Literature-wide novelty remains open.",
  "created_at": "2026-10-17 22:48:33",
  "updated_at": "2026-10-17 22:48:33"
}