{
  "id": 3997,
  "curve_key": "3057789110906359792957201:-10253999864232271435740936799098596345",
  "ainvs": [
    "1",
    "1",
    "1",
    "-63703939810549162353275",
    "11868055398390437520149466551679881"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 170.4414624158134,
  "faltings_height": 12.247205808670202,
  "conductor": "455514655953569565656462935595492873046",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "37",
    "43",
    "71",
    "157",
    "631",
    "12721",
    "1299673",
    "11326561",
    "20456041"
  ],
  "discriminant": "-44302059026454397158902707819785942171747935099609754556932002517086208",
  "regulator": "4264672898283794080.108075246423029782146790107717266125583802689",
  "points": [
    [
      "606291373753531/2209",
      "12740702239957423094602/103823"
    ],
    [
      "-214860421121379989/1283689",
      "194270228276011449978517342/1454419637"
    ],
    [
      "-5332394472259903501/16883881",
      "1527312611801963048419232014/69375867029"
    ],
    [
      "65951039939182919/588289",
      "35343219277989024902933458/451217663"
    ],
    [
      "3471931727793895343569/4913309025",
      "194730713318824099722481639922282/344398396107375"
    ],
    [
      "32234168657830431963179/15689316049",
      "5747433310781240657270333171051966/1965196660349593"
    ],
    [
      "5891385860308257769/85100625",
      "69288261196927339332130918528/785053265625"
    ],
    [
      "334463113032996239318701/225854008081",
      "190957472251661221086999322989237886/107335084654422521"
    ],
    [
      "6189305869374636610699/34661875329",
      "507566802477085969131287527092286/6453243963127233"
    ],
    [
      "96091505789278499/410881",
      "26020638055766179764028934/263374721"
    ],
    [
      "7996251751564752417280199/139860292441",
      "22611295276972785225150033707994160166/52304812306792739"
    ],
    [
      "10737146067711000271/19193161",
      "32707580005246720261694377346/84085238341"
    ],
    [
      "-1842340144533003037499140489/11927685782463025",
      "174881654461860423202346149718847697434106/1302669619023198776883625"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3637 (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 04:42:09",
  "updated_at": "2026-10-05 04:42:09"
}