{
  "id": 4580,
  "curve_key": "198952430280673645531298041:52725959454175623094301481976551448435",
  "ainvs": [
    "1",
    "1",
    "0",
    "-4144842297514034281902042",
    "-61025416036652507316442748053282620"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 181.66532395257104,
  "faltings_height": 13.206995960096982,
  "conductor": "92600993893266656474637251754052208517553081703634",
  "bad_primes": [
    "2",
    "3",
    "19",
    "71",
    "73",
    "97",
    "127",
    "149",
    "151",
    "157",
    "199",
    "271",
    "463",
    "709",
    "941",
    "1217",
    "1423",
    "1783",
    "2087",
    "4481",
    "7487"
  ],
  "discriminant": "4555653297838626585714195878250512679535322497859076881889458254814803682832",
  "regulator": "122677249080005550883.72982551460608399809426506982685409997798006134",
  "points": [
    [
      "-93196970862624/49",
      "332891096336466613506/343"
    ],
    [
      "-1507846474944",
      "1661481777063001230"
    ],
    [
      "-306633556224",
      "1086780426367659534"
    ],
    [
      "-32697549684",
      "-272884231997231526"
    ],
    [
      "-698035133556",
      "-1578638426784504966"
    ],
    [
      "-948990585716",
      "-1737165605610808166"
    ],
    [
      "-1159739621504",
      "-1784955240668783246"
    ],
    [
      "2156757799509",
      "-1015844216878068093"
    ],
    [
      "185035569243788325429/64176121",
      "1777760480292471817275369190752/514114905331"
    ],
    [
      "5607058386141",
      "12368485064031055299"
    ],
    [
      "147030462039301/25",
      "1672320878758602307511/125"
    ],
    [
      "-103326359706176/441",
      "-8772319178101836535478/9261"
    ],
    [
      "-2659365551505339/41209",
      "3798562490655837290778393/8365427"
    ],
    [
      "788045658287337277411133421/46536968883601",
      "21961530377988732381436581318252131901600/317465940867118185401"
    ],
    [
      "851249278022292683413309/161947490329",
      "723906633703005339578045677982233000/65172042690628483"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/2-r15-z2k3.ec.\r\n\r\nSpecialization u = 12/5, t = -159/38 of the Elkies–Klagsbrun Z/2Z family (arXiv:2003.00077). The original submission describes Mestre–Nagao sieving followed by PARI/GP rank calculations.\r\n\r\nSubmitted to ICARM to document these improvements and make the curve available to other researchers.",
  "created_at": "2026-10-18 08:11:02",
  "updated_at": "2026-10-18 08:11:02"
}