{
  "id": 481,
  "curve_key": "968848306898164127756625308751985139289689627341697616:-1113713798614174289651533441456113799198981235286429260804659675350852543152518080",
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  "rank_lower_bound": 18,
  "torsion": [
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  "naive_height": 373.2341854554844,
  "faltings_height": 29.093118081350845,
  "conductor": "53806326363419427086537383779816765270954899278777110096654970448126165901027556398264",
  "bad_primes": [
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    "920478348419602499"
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  "discriminant": "-191511835100981240213910393778202367287469014388481494957834096697504959138311360261067989515132397137021293676057567881393449591491070870462397925022622413568",
  "regulator": "11468189097092191091236.255181345108355748190878849199545439131484346729377",
  "points": [
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      "1088809519885090076951414741896809557/12881569009",
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      "22782340518748659936359216570214096808201018521894/8353070389"
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      "-1432979789658835215103498221291313223/17873283481",
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  ],
  "submitter": "Matthias Breddin",
  "history": [],
  "commentary": "Exact rank 18, unconditional: rational 2-torsion point, 18 independent points with matching 2-descent upper bound (PARI/GP ellrank). Fiber t=-3259/10943 on branch u=22/17 of the Elkies-Klagsbrun Z/2Z rank-9 family (arXiv:2003.00077), found in an exhaustively certified slice search by Matthias Breddin. Listed as 'Breddin (2026)' in Dujella's Z/2Z table. 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 19:28:11",
  "updated_at": "2026-09-01 19:28:11"
}