{
  "id": 62,
  "curve_key": "0:785203836448278982564891253072185632",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-908800736629952526116772283648363"
  ],
  "rank_lower_bound": 17,
  "naive_height": 165.30250283428862,
  "faltings_height": 11.832864478649013,
  "conductor": "29733076040369196065644941545122876271020366852499870815169972871684",
  "bad_primes": [
    "2",
    "3",
    "2195745961",
    "413891567044514092637683"
  ],
  "discriminant": "-356796912484430352787739298541474515252244402229998449782039674460208",
  "regulator": "3160234672289479672416233508.12027866509734322914490119491393668142907407",
  "points": [
    [
      "298790075644804342283980784868871/338043529350370813225",
      "5161349606204399690920252276261178070200995539294/6215254847769749632414964520875"
    ],
    [
      "270591370675628585666599951092583/1330170417506751082249",
      "4204011896288889911631034546142768651699741660430/48513312301533384558486215185307"
    ],
    [
      "325711162975741591923445133588371/1052929463779991398225",
      "-5787321283665994825424977201858275717685219519956/34166376148636124826781558558375"
    ],
    [
      "1211712532726128720491413342757359/16223941796409657025",
      "42179303035772843722884231140233126307757275471898/65348341423942992849106321375"
    ],
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      "-45511555930423359204879858346721593921694733454080/214520974960756038450867149698709"
    ],
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      "1193485252300183998204780009216121/12129239979490109440000",
      "8849454084306730092832158704556981698570573221581/1335827510135299734248783872000000"
    ],
    [
      "2593675287800486498913879030036859/25807176887944349617225",
      "-42751818514177766312939758214885318731526695289148/4145822916881649392274547955517125"
    ],
    [
      "3077300921695987166539964733710863/31522550027409402194689",
      "-25979911623890974715859271180333902196867407684750/5596699818568151395152805066539137"
    ],
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    ],
    [
      "11950777486078440569963034830397097/67332468107359410846916",
      "1195575217084807112146406927423399551700384025930165/17471765860802684591886166103771464"
    ],
    [
      "32897935731038035198457842129038763/208286420018823947157289",
      "5233788033009907864404702853919512596771275642180280/95058604246594295490906437252522837"
    ],
    [
      "20633518747541148948800944355581657/140573422665650005479396",
      "2502007264930004827301247855826744471532652889922755/52705365409812184960750748589475944"
    ],
    [
      "61238135983124397127054621223243257/626138814511227732809796",
      "-2561146939700617106205336638889703164869384364340525/495456967270561665445673889123955656"
    ],
    [
      "2324524904636311085961808350770265673/9878844188981889047430144",
      "3418217044393581168928235873217774854469695847280879045/31049828344088581964714849238008758272"
    ],
    [
      "6916737030865166929678826270687531593/20533409506285541218903104",
      "17973246213956629567348995135636986789359373964277484485/93044692048178135854894591156891848192"
    ],
    [
      "1194537640939104093442656918171419153359/234178544464776436764868225",
      "41285568778238657684933397401332433223076982094874752397602/3583609287614365760517866287425122866625"
    ],
    [
      "28221301625148907160620412386322712252871/1214634268989054295088514025",
      "4740951854035394390115339947785818419239050274616667906265794/42331951983322992425954355521097926555125"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Noam D. Elkies, Mordell curves with large rank, and Elkies, ANTS XVI, section 4.2. This is the lower-height member E_k: y^2 = x^3 + k with k = -908800736629952526116772283648363 from a 3-isogenous rank-17 pair. The submitted rational points are dual-3-isogeny images of Elkies’s 17 independent integral points on E_{-27k}.",
  "created_at": "2026-05-29 04:06:13",
  "updated_at": "2026-07-01 22:35:40"
}