{
  "id": 5596,
  "curve_key": "0:-157878718167036642048",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "182729997878514632"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 93.0167176112426,
  "faltings_height": 5.809049043395178,
  "conductor": "36289369535338444294503260444736",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "978917",
    "2817677"
  ],
  "discriminant": "-14424588917862607545733511987657223168",
  "regulator": "220621755481297099.776963805374801153999321376892717465302490",
  "points": [
    [
      "-4913690969522/11744329",
      "13317806344172830200/40247815483"
    ],
    [
      "1912327053341506/5173205625",
      "179698464171509815118404/372082814578125"
    ],
    [
      "2777664070323874/5080125625",
      "213044317208714054002932/362085953921875"
    ],
    [
      "3535427736203938/1505207209",
      "211691642155539263411940/58397524087573"
    ],
    [
      "4982584555946339339209/2879834555528100",
      "357858441931638477151677117987323/154543700772969955929000"
    ],
    [
      "23752111274277661992649/7776804988578025",
      "3672329090844289585978420622978607/685806841199714485364875"
    ],
    [
      "-3529076583934934804420098862/8183761223545719749809",
      "237068820629080424529141385891200867038460/740336948084374609218998682879127"
    ],
    [
      "-41903233002267147068182743564983/234324526247825023386759681",
      "1509132052843998745039228715559054196353391726415/3586960725264549738925674946812761404671"
    ],
    [
      "777348733267906874386440306909470713/1904311289810069210553818390784",
      "1315912483002931334128101892692600063438680168573897485/2627888372045310356712860916053938071259901952"
    ],
    [
      "30111507590940830611128836795459314/48214884812955452002922428225",
      "6912545812287099995251998437719313994330283286199012/10586970436299842560839228416308631687014625"
    ],
    [
      "-167496803649882470783732922715388039/345637505662230707946948405625",
      "53348630178563671642300976983255009416618585233410041/203203551227267488311829938470509216495421875"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of jesper-petersen’s curve #5586: https://elliptic-rank.icarm.cloud/curve/5586.\r\n\r\nThe source is the specialization t = 11/9 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with Bruin–Nasserden rational parametrization parameters (u,v,w) = (5,4,-2). Jesper-petersen describes varying these parameters, applying a sixth-power-residue Mestre–Nagao sieve, deduplicating through 3-isogenies, and selecting candidates by conductor.\r\n\r\nStarting from y^2 = x^3 + B with B = -4933709942719895064, the rational 3-isogeny\r\nX = (x^3 + 4B)/x^2,\r\nY = y(x^3 - 8B)/x^3\r\ngives Y^2 = X^3 - 27B = X^3 + 133210168453437166728.\r\n\r\nThe 11 submitted points are the exact images of the source’s independent witness points. Every image was checked on the resulting model. Independence modulo torsion is preserved by the isogeny, giving rank at least 11.",
  "created_at": "2026-10-23 21:41:31",
  "updated_at": "2026-10-23 21:41:31"
}