{
  "id": 4003,
  "curve_key": "45947999951506667052925990921:1929655091921498535095283349721604342344219",
  "ainvs": [
    "1",
    "0",
    "1",
    "-957249998989722230269291478",
    "-2233397097131443816082419687178453392744"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 197.991923496201,
  "faltings_height": 14.565193343614991,
  "conductor": "4858903795077400145101018027817292162914370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "37",
    "67",
    "103",
    "229",
    "271",
    "631",
    "643",
    "1093",
    "1103",
    "1193",
    "1237",
    "1489",
    "2293",
    "19843"
  ],
  "discriminant": "53983048570875774740525271809583428053599358575990413808988770782244687155894010000",
  "regulator": "6487225235337241158270.68216740473885625079302905424341466004412313",
  "points": [
    [
      "-1361278550053487880249163995/48134331527881",
      "15732159160861853979836686676341184013787/333950745498301838971"
    ],
    [
      "-155059079827794491306055/22468810816",
      "214178405795602248901830031244025127/3367984866075136"
    ],
    [
      "-2682947943672907932184210/282108637321",
      "11616328968521372057862608736600728028/149838899518038619"
    ],
    [
      "716187499591874921205/22174681",
      "-2427272395298280949432776004387/104420572829"
    ],
    [
      "-1628435019821927179633410/470970630529",
      "-10398609453203688291984651717149186476/323214427525028417"
    ],
    [
      "-523420889872127303410114064335131/172294300511989446025",
      "57509234695918683415332277350502622852905278488443/2261550900760497253309437638875"
    ],
    [
      "-21233724933258593172403419/9015192405961",
      "77385447329538595836858882715979509499/27068394669862487291"
    ],
    [
      "-1519290464871018566161554775/64850631834121",
      "-44725397512972109273749493635838679717387/522241424803226237669"
    ],
    [
      "2647484481346247029256235642414/31283473389594409",
      "-4001011468146731485860270217099052713830557668/5533150077256218903498923"
    ],
    [
      "2291205990784683476694030/736525321",
      "-3467965044605438066988238362244898657/19988560686619"
    ],
    [
      "4033100076491435438875160732093745/3734325466685522944",
      "256023497050828567993343309196263468202684832061159/7216360980327506363333967872"
    ],
    [
      "-6519354405981770537864007573210/690100332226591729",
      "-44282521139319985994335898738177027947962467939/573282064395896874360111433"
    ],
    [
      "21696126292770731331478773182012026030/230196664187134840621881",
      "95315569175293882895270887423764787751673842003816870788/110445630520624794443240629028530029"
    ],
    [
      "50480422704150412098198122641510479539145/526109874906179070145300489",
      "10720887367888138727100156220485692752166683882950133489450411/12067426995857467705252219765357570548763"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3641 (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 04:43:46",
  "updated_at": "2026-10-05 04:43:46"
}