{
  "id": 5053,
  "curve_key": "2784523229716140765040310906167488:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-58010900619086265938339810545156",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 231.0281542059757,
  "faltings_height": 17.3205865954728,
  "conductor": "928174409905380255013436968722496",
  "bad_primes": [
    "2",
    "13",
    "53",
    "61",
    "1049",
    "2203",
    "39209"
  ],
  "discriminant": "12494209902361742735086819498697817049767824272563377793991421041957942818634923696494142282010624",
  "regulator": "26469833199.00466735590707397429714375638253943540592",
  "points": [
    [
      "-6630781716224644296401654/2119405369",
      "37898524807046727305935501089494234040/97571064972653"
    ],
    [
      "-47959503705388406/25",
      "40355252772076974950450328/125"
    ],
    [
      "-2012369763426013460703016016078/408976726187929",
      "3372936566409678481200200962922513596582189344/8270807086672118678717"
    ],
    [
      "14367866432533013088026466453/1642849737169",
      "846450798696590930283655136383738791340827/2105701293569782553"
    ],
    [
      "117995513044227133795416079244401/450027177256336",
      "1281194088660299280511666189048097856608790452745/9546806334076259915584"
    ],
    [
      "113068860380488414690384383157/7063704164169",
      "33440362264229828518927516458960880604489141/18773651570474293947"
    ],
    [
      "11050833054617576728085564813607361/216241706842705296",
      "1148721515899435589086781050415332173004781411416415/100556278247879684997937344"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 7616488732945534, rank 7 example from Watkins, Donnelly, Elkies, Fisher, Granville, Rogers, 'Ranks of quadratic twists of elliptic curves', Publ. Math. Besancon 2014, doi:10.5802/pmb.9; points from https://magma.maths.usyd.edu.au/~watkins/PTS.r6r7.",
  "created_at": "2026-10-21 01:50:20",
  "updated_at": "2026-10-21 01:50:20"
}