{
  "id": 4923,
  "curve_key": "0:957031541732794132512",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-1107675395524067283"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 96.62073604754215,
  "faltings_height": 6.109383913086808,
  "conductor": "60589865770340686157128399363506276",
  "bad_primes": [
    "2",
    "3",
    "25969",
    "164357",
    "9611813"
  ],
  "discriminant": "-530040145758940322502559237631952902448",
  "regulator": "13836989833967245.338897297773386611864750129473908840620785240",
  "points": [
    [
      "123108877178208543/118884971209",
      "2147450660000624830400370/40991181417949573"
    ],
    [
      "30782835583129803/29710382689",
      "346244602550944871914200/5121089532954863"
    ],
    [
      "31064016080570779/29164100625",
      "1581024433704070519564208/4980499284234375"
    ],
    [
      "32637794522594367/26005110121",
      "3909812152259471639052510/4193610063222581"
    ],
    [
      "130919613739938363/103257467569",
      "32007323155280523612192360/33180444856219753"
    ],
    [
      "32903467707711529/25453011600",
      "4166187102515421128072917/4060773470664000"
    ],
    [
      "35457844971513529/19788048900",
      "5999752989700423825491917/2783584838763000"
    ],
    [
      "39442313740159657/8555510016",
      "7788875944505145545935765/791350454439936"
    ],
    [
      "40499866018553779/4100481225",
      "8145741018018381083275708/262574315242875"
    ],
    [
      "163855249393035423/3913378249",
      "66326527755044413124683950/244809203122693"
    ],
    [
      "164003374977208843/2106534609",
      "66416910282873909133035580/96683618949273"
    ],
    [
      "164440053912792991/4871342025",
      "-66681469585831145792589586/339995316634875"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4753, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4753.\r\n\r\nThe source commentary attributes the original Mordell curve y^2 = x^3 + 41025014649039529 to Noam D. Elkies, “j=0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields”, NMBRTHRY post, 30 December 2009: https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;6a3fad67.0912&S=.\r\n\r\nApplied the standard degree-3 isogeny from y^2 = x^3 + B to y^2 = x^3 - 27*B. Here B = 41025014649039529, giving y^2 = x^3 - 1107675395524067283. The coordinate map is X = (x^3+4*B)/x^2, Y = y*(x^3-8*B)/x^3.\r\n\r\nTwelve 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 60589865770340686157128399363506276. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:56:34",
  "updated_at": "2026-10-20 22:56:34"
}