{
  "id": 4924,
  "curve_key": "0:-5302427732230307485536",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "6137069134525818849"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 100.04490346247863,
  "faltings_height": 6.394731197664847,
  "conductor": "5579795194362886401899718369476101452",
  "bad_primes": [
    "2",
    "3",
    "29",
    "26814493",
    "292300571"
  ],
  "discriminant": "-16270682786762176747939578765392311834032",
  "regulator": "317639787993803296.75564786661274983627959256497835566702193949",
  "points": [
    [
      "-588222328839118361/468790810489",
      "654779037130535353843553840/320973098498039987"
    ],
    [
      "-412991107489478645/626768305969",
      "1200258681823922946650004646/496204319847679703"
    ],
    [
      "898213057702712695/1483784663449",
      "4557717209797610535274513724/1807408485039871043"
    ],
    [
      "1062395275706150635/1572332921329",
      "5005490852034956611363195106/1971590703043308983"
    ],
    [
      "2198281090787001163/2129471851441",
      "8359731969501312748167651926/3107476518124159511"
    ],
    [
      "81869082420540156139/18993759061489",
      "768624768919122591703746348190/82778277847877314487"
    ],
    [
      "144614993448455516683/27666663727921",
      "1776055073695333729292207246374/145524188875792675031"
    ],
    [
      "1649640368728255366196983/13961315563476121",
      "2118774422314605366818393242444158124/1649641277923682703355331"
    ],
    [
      "4556573422331007264440203/27484782606193201",
      "9726528226784482328444761336127500474/4556574331526434601598551"
    ],
    [
      "4576005126095092092793639/27562867183786489",
      "9788813283713283327086917615990514440/4576006035290519429951987"
    ],
    [
      "42410161958251425265/86520990375556",
      "2012752597864819407093211326103/804789354462636476296"
    ],
    [
      "1483376091408988471225/533786775838276",
      "64787502015280488010979552609843/12332516790068532843976"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4754, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/4754.\r\n\r\nThe source commentary attributes the original Mordell curve y^2 = x^3 - 227298856834289587 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 = -227298856834289587, giving y^2 = x^3 + 6137069134525818849. 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 5579795194362886401899718369476101452. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:57:53",
  "updated_at": "2026-10-20 22:57:53"
}