{
  "id": 523,
  "curve_key": "436890603241648127091644819187403193266634971549921:-7758323383453275419874699162228188140842563874460233302256865968767755061969",
  "ainvs": [
    "1",
    "1",
    "1",
    "-9101887567534335981075933733070899859721561907290",
    "8979540953070920624854972089755397949631493850838066431403838505793366247"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 349.8113018749172,
  "faltings_height": 27.145306436091282,
  "conductor": "672417291022846025967500274607123896588697929943810266449219368332393071485129230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "31",
    "43",
    "47",
    "53",
    "67",
    "71",
    "79",
    "139",
    "229",
    "293",
    "419",
    "691",
    "701",
    "823",
    "983",
    "1249",
    "1481",
    "1889",
    "4789",
    "9349",
    "10177",
    "10487",
    "13751",
    "34871",
    "5931247171"
  ],
  "discriminant": "13425470368869166359458471256690306126271090774376039819588530144271474445267271237417585372856717307414207292458646606967673590054032480665600000000",
  "regulator": "2287792295413576293946149.62792192428147249092881348688560385070613839214",
  "points": [
    [
      "1965886856946901381902783861984097/704849401",
      "43039687001053231928577485308126690477249455147439/18713046747149"
    ],
    [
      "-3897998288554549445644874246063/1510441",
      "7256635366577209319559864099467217412987778119/1856331989"
    ],
    [
      "4195950884949480021762444243/1849",
      "8317842168408592342180922551313221307247/79507"
    ],
    [
      "24318861906034198032348145868337/10426441",
      "22304814216411489597498211105103163868882720919/33666977989"
    ],
    [
      "40905207843711009320221825038457186657/5753374201",
      "261618147697530908218471196024065141574808392854258723921/436399186520051"
    ],
    [
      "17755577175046369608497546697153/5139289",
      "50478192486235193158827779833515317835902779233/11650768163"
    ],
    [
      "13478774469301828578751913674468138737/11728028993641",
      "7720512929957893249743244905858312616391442737774870631/40164054380231835061"
    ],
    [
      "-140460626727529521790440112719493371743/42369437290761",
      "454817491114635798818826843413591611956720738872532615751/275790336193712976741"
    ],
    [
      "5473675075802638849030345347595345321/4178458881",
      "12806114173361561350634737110287196536131111591000390699/270099760526721"
    ],
    [
      "402529174011072617592215087732759383105/114094292709049",
      "5555636482973071403645213246459715856428960307581381657871/1218697388911657930157"
    ],
    [
      "7193522377393114937402002070905203/9569339329",
      "1498408381347757549117656898103879206962334729842657/936101481180767"
    ],
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      "452402469778931536357857978476601417/533059151881",
      "531661997965305971837034649050141467488097652060652759/389191284320685029"
    ],
    [
      "1206829797735185374718628961139873633576055613/56842038219319005409",
      "41519046849161559001113610716964825869911782807072257631780045265317/428552924807756545260487169327"
    ],
    [
      "490387191096644825533370915911989659476929/221634291687769",
      "343406311864177458786920123610561123833959847812021373231037537/3299555472826700269603"
    ],
    [
      "279041632441428032314540947286700424716233/87362702551543329",
      "91270314321180512229922285554909879362817298309295255472251077/25821953255366413216018767"
    ],
    [
      "-55147467718475641251212258817845276646007/23831420486758369",
      "15456144078315469698050692412652021154547318640641626326988773/3678958545840516155657903"
    ],
    [
      "34573334478388184114616590778652625917884697/30852937818472483921",
      "74154384472684086988700805600875508875579938370467950117697644499/171373941682005253627570250969"
    ]
  ],
  "submitter": "Matthias Breddin",
  "history": [],
  "commentary": "Exact rank 17, unconditional: rational 2-torsion point, 17 independent points (Neron-Tate height matrix of rank 17; the archived certificate additionally saturates the lattice at all primes up to 97 — the points listed here are the ellrank output, not the saturated basis) with matching 2-descent upper bound 17 (PARI/GP 2.15.4 ellrank, effort 3). Fiber t=-1640/4903 on branch u=58/37 of the Elkies-Klagsbrun Z/2Z rank-9 family (arXiv:2003.00077), found by a Mestre-Nagao residue-table sieve followed by an exact 2-descent-type upper bound and ellrank (Matthias Breddin, 2026-09-02; method: doi:10.5281/zenodo.22242107).",
  "created_at": "2026-09-02 13:43:03",
  "updated_at": "2026-09-02 13:43:03"
}