{
  "id": 4927,
  "curve_key": "0:29285049381155658144",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-33894733080041271"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 89.64721759932016,
  "faltings_height": 5.528257375734975,
  "conductor": "170200434158110225993761639006732",
  "bad_primes": [
    "2",
    "3",
    "4136633",
    "303473981"
  ],
  "discriminant": "-496304466005049418997808939343630512",
  "regulator": "2530554079514346.26701555168502545920711927577961858150306550",
  "points": [
    [
      "3802125939072355/11413289889",
      "67614936958410005163626/1219315998711537"
    ],
    [
      "3877357622095423/10938858921",
      "118008553081450781346256/1144084315688469"
    ],
    [
      "4085742311337763/9566600481",
      "196286775104683875389606/935699626446129"
    ],
    [
      "4368983119389055/7522613289",
      "262614043446749057940776/652458818394837"
    ],
    [
      "5019320608987843/165096801",
      "355604414550298166965294/2121328796049"
    ],
    [
      "5051264662038223/961682121",
      "-358962755117076370277756/29822724254331"
    ],
    [
      "6120642560730319/10650859209",
      "-433981676287213255223740/1099200622946427"
    ],
    [
      "8558748909398755/23215702689",
      "-450375195007985739483574/3537306971614863"
    ],
    [
      "17545299957664975/53929379529",
      "291228941528388480797884/12523858019881083"
    ],
    [
      "6837921826531224895/3600836422569",
      "17836462980418759835974931456/6832900384593441003"
    ],
    [
      "3544974179010743460903235/23249237663678049",
      "6674513444970224975378759207303871886/3544974173989301523119343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4752, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4752.\r\n\r\nThe source commentary attributes the original Mordell curve y^2 = x^3 + 1255360484445973 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 = 1255360484445973, giving y^2 = x^3 - 33894733080041271. The coordinate map is X = (x^3+4*B)/x^2, Y = y*(x^3-8*B)/x^3.\r\n\r\nEleven 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 170200434158110225993761639006732. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:00:27",
  "updated_at": "2026-10-20 23:00:27"
}