{
  "id": 5791,
  "curve_key": "0:-207163378711512",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "239772429064"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 65.92905773404513,
  "faltings_height": 3.5517440536287226,
  "conductor": "8278677754469394930810441",
  "bad_primes": [
    "3",
    "191",
    "5021412127"
  ],
  "discriminant": "-24836033263408184792431323",
  "regulator": "12774979567631.376279124923852394267893814449656960685388",
  "points": [
    [
      "-88253363294/78411025",
      "338976621989622896/694329626375"
    ],
    [
      "24474722803552/12275088849",
      "676859551386133409119/1359993918847257"
    ],
    [
      "9433910625706/949564225",
      "32324861451681162896/29260821593375"
    ],
    [
      "13593080269911284137/47389979185444",
      "50116303094051214827957007409/326234417531805542872"
    ],
    [
      "14848337738201899456/12566067868225",
      "57215907079515742510943388104/44545014173695414625"
    ],
    [
      "45461229434861401/4320328531600",
      "10643821214829375008040899/8979975666071864000"
    ],
    [
      "496560946907063872/52071853862889",
      "395338000578195446340889949/375754819438477643787"
    ],
    [
      "145509647656121079688/6981018752305081",
      "1778330070727996171030430872792/583281506472801509506771"
    ],
    [
      "1927644909054208070895001/163367371867296636900",
      "2864994989548366635930775178736733999/2088084087260221056053516847000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization at t = 144/83 of a generic rank-four Mordell family constructed using the Burkhardt parametrization with parameters (7, -2, 10).\r\n\r\nThe curve is its rationally 3-isogenous partner.\r\n\r\nThe specialization was identified using an optimized Mestre–Nagao sieve evaluating 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [9,9].",
  "created_at": "2026-10-25 09:29:17",
  "updated_at": "2026-10-25 09:29:17"
}