{
  "id": 4952,
  "curve_key": "0:17555685253516942804872",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-20319080154533498617"
  ],
  "rank_lower_bound": 13,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 102.43932959279395,
  "faltings_height": 6.594266708524458,
  "conductor": "81553583866934729091924419700360328569",
  "bad_primes": [
    "3",
    "190669",
    "15787747861309"
  ],
  "discriminant": "-178357687916986252524038705884688038580403",
  "regulator": "1069948232449120719.204778796483994668787510693801043246406737533",
  "points": [
    [
      "144590374900381364833/52878231714564",
      "-136453299436622942501390866979/384516858444527050488"
    ],
    [
      "144906946715436748833/52645791970564",
      "-279216663860337191491011757429/381984283924083978488"
    ],
    [
      "152075953042332011769/47234692562500",
      "-1172913782736745174503728664103/324632233308921875000"
    ],
    [
      "2380833337180826721/734431860100",
      "-2333694407718185896764549731/629400759787099000"
    ],
    [
      "2406385874111598553/714417133824",
      "-2554533460845280291985185949/603848222856327168"
    ],
    [
      "155634953675753120377/44430836597316",
      "-1409830698211424684794788304103/296160228241553006136"
    ],
    [
      "2511700203799260697/628728469776",
      "-3285632871105314077870572637/498533893168665024"
    ],
    [
      "2529868986546021273/613358381584",
      "-3391625065361748321721471709/480365110421904448"
    ],
    [
      "166518915254029709769/35227904796100",
      "-1931066559857299859325974061103/209088535615340291000"
    ],
    [
      "176290069463437869769/25783138844100",
      "-2265062860746743210362658301103/130919301940075011000"
    ],
    [
      "2868018701661327297/272456856676",
      "-4814563291082098719342647477/142215395306598424"
    ],
    [
      "3008497009082664721/14450444100",
      "-5218238049273482659923338981/1737087885261000"
    ],
    [
      "3725830592764050721/800040802500",
      "6427777600251218925587410019/715596495796125000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #61, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/61.\r\n\r\nThe source commentary attributes the curve to Noam D. Elkies (2009), originally given as y^2 = x^3 + 48163745551486811536 with thirteen independent integral points, and identifies Andrew Sutherland's MIT rank-record page as the source of the original equation",
  "created_at": "2026-10-20 23:41:34",
  "updated_at": "2026-10-20 23:41:34"
}