{
  "id": 4005,
  "curve_key": "-298677828707656820639237664:-16106736924401502563300812000688418511584",
  "ainvs": [
    "0",
    "0",
    "0",
    "6222454764742850429984118",
    "18642056625464702040857421297093076981"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 185.1601125074899,
  "faltings_height": 13.498770517848568,
  "conductor": "85468703986756648905003803597594316557982840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "47",
    "53",
    "61",
    "97",
    "103",
    "163",
    "197",
    "313",
    "463",
    "607",
    "1171",
    "1217",
    "3041",
    "8377",
    "138637"
  ],
  "discriminant": "-165550670784052849205508341887404385684252761598401932258426570200004082750000",
  "regulator": "34480631533548318057699.0748374427632772532635473725529471265048607",
  "points": [
    [
      "-996403803097108612845155960292762399884863/2083449050919399731275249935376",
      "11861359190719957958838599442374650770049170667432156241134469025/3007283191431233401107676153337294425337026624"
    ],
    [
      "-448227613902017373070993119108569266/239426738524654637926225",
      "76998529475747488809673637701692282090320316819363273/117154499876649637697550924286238375"
    ],
    [
      "1105506566249104912341601658438/485209824805021849",
      "2258344105756874867057085248073140514240134325/337982628528456535973869507"
    ],
    [
      "-1201012240579028200560728939/908762927033025",
      "78017583733129250633147339359470789511316/27395290025644826577375"
    ],
    [
      "3055978807482420306327708966/1600325696573041",
      "391974867099160292138808802690896463392655/64019542788832388849911"
    ],
    [
      "3141611395537528368328673670549/159244898611770049",
      "5619416656464539239793307902304951995663037620/63547474130234187186085343"
    ],
    [
      "29134751651432546795824495077/5198772092505121",
      "5678880559011288126232040600388725018911600/374844521986343504458831"
    ],
    [
      "48563863159735605259910908622/162162167272681",
      "10702495549968037752801155921008218829077525/2065020227240996204171"
    ],
    [
      "-116425273892684814667480059375627/86763347837533213729",
      "2268091879153244071452463363201373934935122512700/808173213612989535770100271183"
    ],
    [
      "22547622018483543945913532656963337/9072737641973252229376",
      "6077351294337817567687328178400252905538039385242725/864186601655194601648805634789376"
    ],
    [
      "-26629019776108910225027760038269866/20170109599505056992025",
      "8165792369926082177002362953723158674208419863470277/2864589443264967978126233014416125"
    ],
    [
      "3744780377618705380258159783809340517/4828577956793003756641",
      "7246725047981304760359392063215879733511564105205512600/335528079581406984825059624163311"
    ],
    [
      "79492058121225775673035481359171451177/15176736053241351251959696",
      "825474155651893136468453038652475169703442227632090000725/59124512343557753780172682634333160256"
    ],
    [
      "-2640423753519537367429818412005703/1605044320272403219456",
      "127857430742698441209976007901766322263287926267475/64302897639587590255281442095104"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3644 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 14: 14 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:44:07",
  "updated_at": "2026-10-05 04:44:07"
}