{
  "id": 4008,
  "curve_key": "543830788068313581203795715934801:-82125988678367995544417870097865784356840089332185",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11329808084756532941745744081975",
    "95053227636999993898925564809485431193456615081"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 229.86467795829617,
  "faltings_height": 17.212859860700572,
  "conductor": "44025871847742350339136611296547024333859559593162",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "53",
    "59",
    "137",
    "317",
    "379",
    "419",
    "647",
    "821",
    "1747",
    "2143",
    "2297",
    "4513",
    "5647",
    "10453",
    "191119"
  ],
  "discriminant": "-3810092021633327326305165313748236692206328424470137450671486982205553508062133107232244783787008",
  "regulator": "14992366452696241234122.867365043604287738759853636397568705369499333",
  "points": [
    [
      "97430992988026546329217/451584",
      "30408492470347160499607230276799729/303464448"
    ],
    [
      "173889451938532594820623746/112614607561",
      "10771543756066616272431226101528459430341/37791322619927941"
    ],
    [
      "3288818821442567019684/13225",
      "188591224304622888353462191288647/1520875"
    ],
    [
      "-1498201495698169590857173722/1061891091361",
      "359992381093546043615961358785475708168629/1094258593716774641"
    ],
    [
      "-33486094291674996352105428/6404320729",
      "54593063189836057727447092948499123757/512518574979683"
    ],
    [
      "-77905312488302483444430305037/18789502718596",
      "21664039177865846385201488678077651081722429/81446594381260020856"
    ],
    [
      "-10834933800367794548321527098/5648023174249",
      "4446350131124903367238631126251422478587417/13422849010923680693"
    ],
    [
      "3565130401807069326/961",
      "9610950145695430838963000883/29791"
    ],
    [
      "104573940393282840348464814/69151643089",
      "5187494025359068434261366326749627290843/18184600128185063"
    ],
    [
      "415727235900344322561838/384120801",
      "2182697563566038100286812016908533227/7528383578799"
    ],
    [
      "35595634575824761471116/32478601",
      "53630618644969136733938507646625479/185095547099"
    ],
    [
      "-1264917665674414217092242/544242241",
      "4188558446092161222192467414289181797/12696627240289"
    ],
    [
      "1496804195555085562653288462/283821409",
      "57909177867004055567673998334655216755819/4781539277423"
    ],
    [
      "10192137436108865471649261/3028961296",
      "51388742016483576286686129412611036351/166701913886656"
    ],
    [
      "583438125846676892150052517759782/34722611625241849",
      "13950338224480677165819615145695752910456832234671/6470212943319866028059507"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3646 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 15: 15 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 04:44:44",
  "updated_at": "2026-10-05 04:44:44"
}