{
  "id": 4921,
  "curve_key": "0:-289219089346813698077952",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "334744316373626965368"
  ],
  "rank_lower_bound": 13,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 108.04294289680892,
  "faltings_height": 7.061234483859039,
  "conductor": "4150139160905439335634474289855580421312",
  "bad_primes": [
    "2",
    "3",
    "174900953",
    "8860684741"
  ],
  "discriminant": "-48407223172801044410840508116875490034183168",
  "regulator": "6466793116832014257.394781788733204745296872147069469108037305346",
  "points": [
    [
      "-36430494400452669623/5574401274289",
      "98153482505037209862074029655/13161256173417991913"
    ],
    [
      "-7173187810203168938/1896809299009",
      "43764938198562045109556678140/2612374916632248223"
    ],
    [
      "-26893655107378045127/8016650414161",
      "391165077033802161600605020495/22698095466492616409"
    ],
    [
      "-1780024149363490634/3043262805025",
      "97103737587578732996441246164/5308956747052087375"
    ],
    [
      "9091852464115604089/15101190300625",
      "1074026255860197859982376321937/58683603037986265625"
    ],
    [
      "4976057525469422866/4225840819225",
      "159324616945094250848976410336/8686997584468544125"
    ],
    [
      "33398336136361619737/19026145438609",
      "1530606712046936716778104996865/82990086710232281273"
    ],
    [
      "21793601746457051218/6636296362201",
      "328915299867337180466065007920/17095769694962358301"
    ],
    [
      "67187274167873518198/11655607668961",
      "912876476835337030800221678900/39792605905670591791"
    ],
    [
      "109505189928830977366/15487806057025",
      "1598976353443018553001054204164/60951563786149321375"
    ],
    [
      "544183359761328058657/70644983173249",
      "16708454638357186811494657983205/593775110335198720193"
    ],
    [
      "199694467582549453078/22404233022721",
      "3424596144063181062036989960420/106046202613008559231"
    ],
    [
      "1075404073155201721366/66631548724225",
      "36643213778619626795886289368164/543901005399334693375"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4755, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4755.\r\n\r\nThe source commentary attributes the original Mordell curve y^2 = x^3 - 12397937643467665384 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 = -12397937643467665384, giving y^2 = x^3 + 334744316373626965368. The coordinate map is X = (x^3+4*B)/x^2, Y = y*(x^3-8*B)/x^3.\r\n\r\nThirteen 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 4150139160905439335634474289855580421312. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:55:04",
  "updated_at": "2026-10-20 22:55:04"
}