{
  "id": 4959,
  "curve_key": "0:-2794167253180570663841260266071426232",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "3233989876366401231297754937582669"
  ],
  "rank_lower_bound": 14,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 167.84119493676462,
  "faltings_height": 12.044422153855349,
  "conductor": "116790896991187197972944027924327549003781191857801594054651281",
  "bad_primes": [
    "3",
    "7",
    "19",
    "23",
    "53",
    "307289",
    "711959",
    "101560749485011"
  ],
  "discriminant": "-4518154304830240324391230912068151441335085594563790792747972876514883",
  "regulator": "805348304786457847735130713.348977402298928468503518184462239474130",
  "points": [
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    [
      "-4676659680335102604064026494407699326349564390054407256589971070020686945328872214692939069071010543756214263/46168329185556372010071233030926123619925641907080443206657982624612603677375338150933380904489764",
      "14695852671193256678729868366254131093567999792400526861584452780905292308633984660871192351863156148453037490006347658500279685753382904132997318737406361858721441/313701241040103775850992332849659541453399425463688976498651010137432223239242684473029109934665540133182291719506656244896688793667261264363568088"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4886, submitted by Maksym Voznyy: https://elliptic-rank.icarm.cloud/curve/4886.\r\n\r\nThe source commentary credits “Reynya - Voznyy (2026)”. The source model is y^2 + y = x^3 - 119777402828385230788805738428988.\r\n\r\nCompleted the square with Y = y + 1/2 and B = -119777402828385230788805738428988 + 1/4. Applied the degree-3 isogeny X = (x^3 + 4B)/x^2, V = Y*(x^3 - 8B)/x^3, then set y' = V - 1/2. The resulting model is y'^2 + y' = X^3 + 3233989876366401231297754937582669.\r\n\r\nFourteen supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 116790896991187197972944027924327549003781191857801594054651281. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:52:38",
  "updated_at": "2026-10-20 23:52:38"
}