{
  "id": 325,
  "curve_key": "486935133223470044616436975538374438647887641059134710878736:-328506871651358908839426279438781513615526291577394534770203955115996628252915523280686016",
  "ainvs": [
    "0",
    "1",
    "0",
    "-10144481942155625929509103657049467471830992522065306476640",
    "380216286633517255601187823421134146777992443645481380690941792226978359266852679415988"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    4
  ],
  "naive_height": 412.30644365461603,
  "faltings_height": 32.27863615958448,
  "conductor": "349432175747971837118686050547170875372336606890306428283195130479920",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "101",
    "131",
    "139",
    "149",
    "157",
    "179",
    "653",
    "829",
    "953",
    "1307",
    "4019",
    "7207",
    "29287",
    "44249",
    "121178117",
    "3622521358583"
  ],
  "discriminant": "4362494941807848704026559610365890975197207337251115281214370363978888613665527680012511255596630140495384679977316682533728496642675860125703755399138653218414361000000000000",
  "regulator": "34430367495376806.82338143341906110207956966312996387696791856339",
  "points": [
    [
      "98797428465597921854659966106",
      "18501960057154462753965244476587904114894120"
    ],
    [
      "70608658515713292144980020271",
      "3994161829276020893108640059675171105221650"
    ],
    [
      "46520024909903078786877295346",
      "2994880885411491385752108474380838770935200"
    ],
    [
      "-57720943255918350284108413429",
      "27811078111529201124489016436115090724245000"
    ],
    [
      "-764989076382421108633641129991/64",
      "11445977979062421025994112960416678952063818835/512"
    ],
    [
      "25388143782459322232605563700586/841",
      "245694376936377578672166940167101852223554925000/24389"
    ],
    [
      "-86863614263322156691238785918",
      "24616898901745765937901875786280291487546560"
    ],
    [
      "7628383854510617586079154579444/169",
      "8301959381108234271133955319370381943077235670/2197"
    ],
    [
      "-68409654340863990558041719868",
      "27459930105477512767395593422236922524531870"
    ],
    [
      "195044948131617038220488149956412394/5139289",
      "82283431133081348768684829999230925995889629338125000/11650768163"
    ],
    [
      "3414368457420016094738135714485154/76729",
      "87404877035492432837436131608169349969327057276480/21253933"
    ],
    [
      "16335531540912726198847501141979/49",
      "63292804053841425659456731624558368649977060000/343"
    ],
    [
      "-84774382922118921353920367428877473/877969",
      "17634527581279166417560235769165452719051524269905614/822656953"
    ]
  ],
  "submitter": "Jack Cheng",
  "commentary": "Li's 2026 elliptic curve over Q with torsion Z/4Z and rank at least 13, with all 13 published independent witnesses. Source and maintained record table: https://web.math.pmf.unizg.hr/~duje/tors/z4.html. This is a documented existing world-record curve newly added to this leaderboard, not a claim of a newly discovered world rank record. Exact local preflight re-certifies every witness, independence modulo torsion, the global minimal model, torsion, and the complete bad-prime set.",
  "created_at": "2026-08-24 13:51:15",
  "updated_at": "2026-08-24 13:51:15"
}