{
  "id": 483,
  "curve_key": "12891852158520094749359150846912820278158512503761698961:-46111679277042843820211770547269198122962655844315844619018948591156254208095018041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-268580253302501973944982309310683755794969010495035395",
    "53369999163244032199319178851772476718961242731802220310937173812405654458857025"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 380.688571553623,
  "faltings_height": 29.54891579614793,
  "conductor": "7063699993905304395318647806097462125358626581250568524161592201139470720695407656860165270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "31",
    "41",
    "43",
    "53",
    "73",
    "131",
    "149",
    "179",
    "197",
    "277",
    "463",
    "661",
    "2459",
    "3491",
    "31727",
    "19244683",
    "54275107",
    "196645627",
    "116472563371",
    "117763093086091"
  ],
  "discriminant": "9454256943012350934702661920675584939579298706938543859673337210713612369846625557656301263594391544316105011524245447139937687162888903902605143572582400000000",
  "regulator": "52444020861068508565.62053828799327271421976996051831081831962818096236",
  "points": [
    [
      "-139291217851561028139805650",
      "9385005886345300525380242203756104645705"
    ],
    [
      "269225166767042949115137390",
      "758594411532241394966630854354750216905"
    ],
    [
      "335438250799717991736200526",
      "1010457813249357395013510626814990464937"
    ],
    [
      "54724115460483571535545619160/169",
      "1306266520584792583115984193326735706705285/2197"
    ],
    [
      "14173911517019862289967190",
      "7040313484018062416268931623356609017905"
    ],
    [
      "385271275362245872147090350",
      "2661030218686936270326513730505618823945"
    ],
    [
      "512440124316043215885069690",
      "7092450510303323830685670818890610130405"
    ],
    [
      "478365962914660898584516590",
      "5861462427338199001682920784359342600905"
    ],
    [
      "1881516690433737539486797860",
      "78795929586005385103779968242488710794185"
    ],
    [
      "-150361029184488335995007666195581410/885598081",
      "255620391045058348891571455100867773275608038242922695/26354513292479"
    ],
    [
      "69571280300618504723193047910/289",
      "8020540069312968700760437486032303185792265/4913"
    ],
    [
      "314236939272097380967332810",
      "37988252712091540271952609560328881205"
    ],
    [
      "8977851054808501036809990060630/1369",
      "26818815392208276587716370493548495691173122965/50653"
    ],
    [
      "17759702643194285056144960965/16",
      "2144537929565495132650751292817717157311845/64"
    ],
    [
      "2863077463497444262604620802190/7921",
      "1321548759762463499879509949187436379090580945/704969"
    ],
    [
      "-137399075376770637314330310",
      "9363695230748150021997939119400318762405"
    ]
  ],
  "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=6345/5704 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 19:28:19",
  "updated_at": "2026-09-02 05:26:49"
}