{
  "id": 4197,
  "curve_key": "31228115458601728547953:-2742259556576889399862715506253225",
  "ainvs": [
    "1",
    "1",
    "1",
    "-650585738720869344749",
    "3173911523544766821670373312666"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "naive_height": 155.38681733521292,
  "faltings_height": 11.000102491533765,
  "conductor": "1294818559182185565003",
  "bad_primes": [
    "3",
    "7",
    "17",
    "19",
    "23",
    "103",
    "137",
    "139",
    "149",
    "223",
    "347",
    "367"
  ],
  "discriminant": "13271713351554838582136769683082996758130874765335979124779167009",
  "regulator": "574271.4382506085043501254883240251603007688762081773",
  "points": [
    [
      "-26480400159",
      "1354014220930939"
    ],
    [
      "24489986028",
      "1388935407899026"
    ],
    [
      "242443568904",
      "118726480773418105"
    ],
    [
      "-80433792432507/6889",
      "1732272356985529145975/571787"
    ],
    [
      "122089063749/25",
      "42057012853612133/125"
    ],
    [
      "10042844118486/3025",
      "170531506633188342151/166375"
    ],
    [
      "4323804644773293/3964081",
      "12392920626800488070592995/7892485271"
    ]
  ],
  "submitter": "Manvir Jaswal",
  "history": [],
  "commentary": "AI-assisted (Claude) search: Mestre-Nagao sieve over the universal Z/2xZ/4 family y^2 = x(x+a^2)(x+b^2) with (a,b) = (448324, 264607), then 2-descent (PARI ellrank, checked with mwrank). Rank exactly 7.",
  "created_at": "2026-10-12 08:26:28",
  "updated_at": "2026-10-12 08:26:28"
}