{
  "id": 488,
  "curve_key": "5845428903238231306114694875361958125329468807681:-13552285183624956928528453255105665217172909012139892001388629295347517185",
  "ainvs": [
    "1",
    "1",
    "1",
    "-121779768817463152210722809903374127611030600160",
    "15685515258825181630241214599987142280599667999917044892017001532791041"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 336.86923330636944,
  "faltings_height": 26.002377701791026,
  "conductor": "46280630592701913424698071736504337159840138785939421143334596914282051671126722",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "23",
    "29",
    "31",
    "43",
    "47",
    "53",
    "89",
    "107",
    "127",
    "131",
    "271",
    "317",
    "347",
    "349",
    "379",
    "401",
    "751",
    "967",
    "1049",
    "1721",
    "2620589",
    "3222413",
    "29174072025857701"
  ],
  "discriminant": "9298758585267493634514928795257927126758939209477780337161389303610313499566171351220390957926145388738891430167969425490514686106528117686272",
  "regulator": "2881538532718811151.846872016209351345832644220272879491749646965549491",
  "points": [
    [
      "866871280602900669827229",
      "749361238882963427243457247908453301"
    ],
    [
      "92813910499009763172069",
      "71987477286354434148551569995249829"
    ],
    [
      "237903664049574060821397",
      "13363012937768642040652384897378549"
    ],
    [
      "1238538719886776603145237",
      "1328438144481888597342688799491158133"
    ],
    [
      "20219720442843424429796013/121",
      "1763612415514024659389107429646357519/1331"
    ],
    [
      "35720887681824294807433",
      "106681830777951127169905291838393009"
    ],
    [
      "531556305821754784724073",
      "318033119387493073854035480881430737"
    ],
    [
      "-317584502864035818037227",
      "149430037709953671220424632860105589"
    ],
    [
      "501103878659494177171701",
      "283709250684372126767784669938984821"
    ],
    [
      "9980229851043359249017554327/36481",
      "371636303067395280960636881379129369882569/6967871"
    ],
    [
      "42556093513403717423655677/169",
      "69024694887207049532644828403481128729/2197"
    ],
    [
      "-3454074126422370405526547/9",
      "2072923329126651669609910877814867911/27"
    ],
    [
      "29837567122316228561773242253/34969",
      "4774017106676815453913595388342953882842399/6539203"
    ],
    [
      "1099767006275272834927371106997/1274641",
      "1070066136824834915599440320329425368908046077/1439069689"
    ],
    [
      "615704516845546471377497723989/1404225",
      "359152816673264344687724688153249635772111317/1664006625"
    ],
    [
      "324618986517462653231893339/100",
      "5816175556439315462801067500762400412493/1000"
    ]
  ],
  "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=-2794/8565 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. 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 19:28:39",
  "updated_at": "2026-09-01 19:28:39"
}