{
  "id": 484,
  "curve_key": "1624626917453694454132218775790524583945432665904401374721:-64189959855293597164262928549418813344718282308689448303323794670330346941204842548481",
  "ainvs": [
    "1",
    "0",
    "0",
    "-33846394113618634461087891162302595498863180539675028640",
    "74293935017700922643822833966414204824696459059596203865321768280569673544384537600"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 395.19788550247017,
  "faltings_height": 30.828701697690637,
  "conductor": "45137010909088824799547895561717868348558143392087086144356474853426870259431025549767699410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "31",
    "47",
    "53",
    "67",
    "73",
    "101",
    "103",
    "373",
    "439",
    "523",
    "557",
    "823",
    "6871",
    "16573",
    "32257",
    "1025009",
    "13078867",
    "341910589",
    "1050385466742442173865787"
  ],
  "discriminant": "97054307859641822030350672034695968444864497945208558276096460142227212066598782632200926616220498378460728516083657024809944976744775699798135517801596326626304000000",
  "regulator": "63571135768406371937.68441165023138172105475726412682389447714063831331",
  "points": [
    [
      "7386595899278409033364630530",
      "476770657287089269189318166857113860101410"
    ],
    [
      "2755110347857587508882489440",
      "44231391140666971718822174737288202844000"
    ],
    [
      "40595183036697876184944393795/4",
      "7047723133855597014603939949486204845222855/8"
    ],
    [
      "-6586160985433357634655304470",
      "107333258767229056008153516914749194436410"
    ],
    [
      "4168624738593478792964697120",
      "75106677548545912486311854566315322309760"
    ],
    [
      "576196751029756617038780117176/81",
      "320667896135524524169951616601073102642049768/729"
    ],
    [
      "67849435203014859286788612816/25",
      "6156623939943514087205074902739414433547024/125"
    ],
    [
      "5062393861651124120685055680",
      "180799155557292293625818776297367662097760"
    ],
    [
      "195575672428164891807536161021320/26569",
      "2049718056565933246819269494738201235384942551520/4330747"
    ],
    [
      "260407906448336515639344060121695/58564",
      "1533686216451852556626637025033839755462110607405/14172488"
    ],
    [
      "315851764190557744432080252218940/109561",
      "944557743011590032769800844973796147006461751900/36264691"
    ],
    [
      "13309872490000139715878271536252150144314560/4796440214657569",
      "13856423623883705472511073487227365811978535558119819572473669600/332183879906676938264753"
    ],
    [
      "-163080158700803596197500516058480/27889",
      "1252048318903855868796684886112299309951442078880/4657463"
    ],
    [
      "-427166496999306101990106971621068080/172843609",
      "858846874428028069120416076769903289679352787881648880/2272374927523"
    ],
    [
      "304054034292740224346426377422737626980/80787261361",
      "340729079732329548362621565252873892228728585906660252660/22962244083898391"
    ],
    [
      "110057300712275272938631092115552447440/23868087049",
      "470292719591583365073110781368773113439730232213427266960/3687452372461157"
    ]
  ],
  "submitter": "Matthias Breddin",
  "history": [],
  "commentary": "Exact rank 16, unconditional: rational 2-torsion point, 16 independent points with matching 2-descent upper bound (PARI/GP ellrank). Fiber t=9150/16213 on branch u=19/13 of the Elkies-Klagsbrun Z/2Z rank-9 family (arXiv:2003.00077), found in an exhaustively certified slice search by Matthias Breddin. Preprint (proof, measurements, decided slices): https://doi.org/10.5281/zenodo.22242107 — data and code incl. the per-fiber ellrank certificate and witness points for this curve: https://doi.org/10.5281/zenodo.22242109 (Breddin, 2 Sep 2026).",
  "created_at": "2026-09-01 19:28:23",
  "updated_at": "2026-09-02 05:24:56"
}