{
  "id": 4001,
  "curve_key": "66495278128834254636668242123825:-542233284346905397594818469659550861693942675625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1385318294350713638263921710913",
    "627584819845954744074343175234538294770980031"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 219.82405118814216,
  "faltings_height": 15.831467991583617,
  "conductor": "84518160226589403767572961475020918466832050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "47",
    "67",
    "71",
    "79",
    "97",
    "167",
    "173",
    "211",
    "313",
    "367",
    "431",
    "743",
    "1621",
    "4643",
    "5791"
  ],
  "discriminant": "29461828723379382017989879893344413944855161380284598234594602571290086867047056000000",
  "regulator": "116763676981644047990.708409496982368846649434500638169333952583452",
  "points": [
    [
      "41753623735616345446685/17901361",
      "-7606316577844376990633683858208538/75740658391"
    ],
    [
      "39765160348884261709765/25979409",
      "-6058341005182479430596346720972264/132417047673"
    ],
    [
      "70039880621885683135/103041",
      "144084892124013760912374752/33076161"
    ],
    [
      "36403392636091415/49",
      "996815228626896036198576/343"
    ],
    [
      "4356706679230119379/6084",
      "790204191377589435759333631/474552"
    ],
    [
      "51956477363475566567081/76440049",
      "-350729293690569369742167568134/668315348407"
    ],
    [
      "330672885038541584671/18225",
      "6000743697815370752938964568176/2460375"
    ],
    [
      "33772672603345395432098331/49686639025",
      "-31146712807186867938424710057893944/11075400271867625"
    ],
    [
      "8122055524038660165891435/10615386961",
      "4314045705437292871985784165124643012/1093713933978791"
    ],
    [
      "1701044880520061589636321/2497500625",
      "-8747762039676417999709719691833056/124812593734375"
    ],
    [
      "33175764714928730285044328090985/48698193123642241",
      "828150307259841052371389182726982209185771952/10746555142240461138859711"
    ],
    [
      "8500152780311546645791417394915/12504210451239529",
      "-11501427945562236006167743482563375370586044/1398248659534279043211083"
    ],
    [
      "55154896167104140664326325335535/79549866579047881",
      "-14024946665813246912815836365017268168376930672/22436710452622950998774779"
    ],
    [
      "52445513093152773139980391310661935/35358173781415671481",
      "9009083800088645827529894724702470426623089262716072/210249387357781437416487176621"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3643 (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 04:43:20",
  "updated_at": "2026-10-05 04:43:20"
}