{
  "id": 3995,
  "curve_key": "17413548596986040854791121:-115774132579490851546297824942742342169",
  "ainvs": [
    "1",
    "1",
    "1",
    "-362782262437209184474815",
    "133997838633518807791458830597605797"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 175.28940901565784,
  "faltings_height": 12.641543372221664,
  "conductor": "1284522297763555835148164816047706661990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "31",
    "59",
    "73",
    "191",
    "193",
    "487",
    "641",
    "691",
    "751",
    "4951",
    "15161",
    "340519"
  ],
  "discriminant": "-4700989739762807590934684446588261310936156133978958574852586645757920000",
  "regulator": "151459265524179170.8828501662322140012386772097013162773610260699",
  "points": [
    [
      "-229881284256260962313/315027001",
      "563560942049416499731831195874/5591414240749"
    ],
    [
      "-4947419586539801/7225",
      "152088968843863712898398/614125"
    ],
    [
      "-835752418814066903/2070721",
      "1380609530732579105330587774/2979767519"
    ],
    [
      "62150705714154883/31684",
      "14889509093517192197376677/5639752"
    ],
    [
      "402532241883095/169",
      "7854878776802735680686/2197"
    ],
    [
      "-737609894693",
      "16716280373268146"
    ],
    [
      "1564805287150906087/3644281",
      "1666633584489977024000757314/6956932429"
    ],
    [
      "12814859314843/9",
      "42726778700205138862/27"
    ],
    [
      "19175936652449203/3969",
      "2636303391063933467024422/250047"
    ],
    [
      "434527389503975/24964",
      "1409441598000510494337021/3944312"
    ],
    [
      "5551230552495938525/8579041",
      "10365997583626232786215610424/25128011089"
    ],
    [
      "15397528734640955/22201",
      "1537384024320701675859762/3307949"
    ],
    [
      "31136289392193143683/23551609",
      "160220603545094625591296454922/114295958477"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3639 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 13: 13 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 04:41:48",
  "updated_at": "2026-10-05 04:41:48"
}