{
  "id": 61,
  "curve_key": "0:-650210564945071955736",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "752558524241981430"
  ],
  "rank_lower_bound": 13,
  "naive_height": 95.8476558607853,
  "faltings_height": 6.044960564190403,
  "conductor": "81553583866934729091924419700360328569",
  "bad_primes": [
    "3",
    "190669",
    "15787747861309"
  ],
  "discriminant": "-244660751600804187275773259101080985707",
  "regulator": "671098787666.6903251127775215461325395089393390179049329444143585",
  "points": [
    [
      "-3635871/4",
      "-314862269/8"
    ],
    [
      "-3627871/4",
      "-644755819/8"
    ],
    [
      "-3436375/4",
      "-2754036385/8"
    ],
    [
      "-856990",
      "-350938406"
    ],
    [
      "-845232",
      "-385629747"
    ],
    [
      "-3332823/4",
      "-3338220641/8"
    ],
    [
      "-792924",
      "-504008563"
    ],
    [
      "-783172",
      "-521721587"
    ],
    [
      "-2967655/4",
      "-4693365385/8"
    ],
    [
      "-2538855/4",
      "-5639045385/8"
    ],
    [
      "-521974",
      "-781244603"
    ],
    [
      "-120210",
      "-866499531"
    ],
    [
      "894450",
      "-1211674470"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Noam D. Elkies, 2009 rank-13 Mordell curve. Elkies originally gave the model y^2 = x^3 + 48163745551486811536 with 13 independent integral points; this database stores the global minimal model y^2 + y = x^3 + 752558524241981430, with the witness points transformed accordingly. Andrew Sutherland's MIT rank-record page lists the original curve and points.",
  "created_at": "2026-05-29 04:04:59",
  "updated_at": "2026-07-01 22:45:37"
}