{
  "id": 485,
  "curve_key": "3552601076257753231688690486809548853627189583510187681:-6650302225724251579465252774865108698530563402103521154789715669512053891555652465",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-74012522422036525660181051808532267783899782989795577",
    "7697109057551217105862561100522932339919505723035449473880423044947230344156825"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 376.82182516323417,
  "faltings_height": 29.250695139151528,
  "conductor": "44679155598732028875449577292101762747529826674110173050234930184664207968832037401401166671113974",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "41",
    "43",
    "59",
    "73",
    "131",
    "149",
    "157",
    "197",
    "307",
    "353",
    "383",
    "421",
    "647",
    "1879",
    "2797",
    "12409",
    "12413",
    "21961",
    "1610579",
    "3714239",
    "8481911",
    "10050352438462415792051"
  ],
  "discriminant": "353453453909373287457091878916192430970772513287617772441739358270936631500110535138438668977455181501097630167554485167120265729618174723728707120689222582272",
  "regulator": "63983651922206937101.10448645432482410464221248850020524252241632009813",
  "points": [
    [
      "-234275942970124510912958557",
      "3489724411080219976551251281282864684944"
    ],
    [
      "391145372188611490461314555",
      "6212135152830445883819602546473502485804"
    ],
    [
      "511820988010609383125556817/9",
      "51738721949485925070884081865527009105488/27"
    ],
    [
      "106410415896252114110458631",
      "1013069443600706181717430611416244532716"
    ],
    [
      "176128492795918295162824007",
      "353723526903114330324543823299663846060"
    ],
    [
      "7803457151684994457579943",
      "2668338564242129792631342380691975177612"
    ],
    [
      "1721819225497553629049060647/9",
      "19836145538164583088285145655535177045388/27"
    ],
    [
      "225803312245193533244173871",
      "1580474769582930398300200991907901751532"
    ],
    [
      "70112372409773525484242879573/529",
      "5652769379268774563073866099041136475201414/12167"
    ],
    [
      "92407249935493860683980803321/841",
      "23025903832875371818423129503644075481473974/24389"
    ],
    [
      "-4357155635666344430255252469/25",
      "488978657404993807850904487990298356950064/125"
    ],
    [
      "12483796532779087995866541412395/9604",
      "43210357726292792750981740111394847943882861705/941192"
    ],
    [
      "369796616907614443405609826294543/2569609",
      "668464898632400105111385708715598352510376014900/4119083227"
    ],
    [
      "-28766984952441690901365913",
      "3130881722809404512272630316369304766092"
    ],
    [
      "-268279912408772331775050949",
      "2871232102677307722168398394464190005292"
    ],
    [
      "729472481579286269108385026583/5329",
      "140664435845270249111254882333114890012650924/389017"
    ]
  ],
  "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=-12533/7296 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 19:28:27",
  "updated_at": "2026-09-01 19:28:27"
}