{
  "id": 5055,
  "curve_key": "13964893574111369456676170324330928:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-290935282793986863680753548423561",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 235.8655639418105,
  "faltings_height": 17.723704073459032,
  "conductor": "9309929049407579637784113549553952",
  "bad_primes": [
    "2",
    "7",
    "31",
    "67",
    "107",
    "977",
    "1487",
    "7547"
  ],
  "discriminant": "1576046956989585601402663805276104231194425908163285389159718332625619225881794131482554136864478784",
  "regulator": "45396935457.19635715968066623565060717986217236807722",
  "points": [
    [
      "-5307214321900018534412367/3639950224",
      "142506413026894970076467631712186182807/219605476914368"
    ],
    [
      "-2457150790226314929152/214369",
      "134223698085495621930146235325728/99252847"
    ],
    [
      "-207915001759990543856950336/250063003969",
      "61429073079322739399977689380651752382040/125047255953750047"
    ],
    [
      "-838380493904195385470439871/255861965584",
      "124010734790998078747960243268385518446305/129422146327423552"
    ],
    [
      "3039532731775075485306619904187392/132833451124518169",
      "111705644594208864931020191512731320605704067293216/48412909578723181939053053"
    ],
    [
      "1499302944197683110138841393493761/65355740379745344",
      "38821691171364667903624042652035908109491124155775/16708043925610139222364672"
    ],
    [
      "-1765100583680914200538734594940638992/11995888183212866862609",
      "271831119947472753336831580057326830191946871176089175828/1313858555450997669945388067726727"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 17056825108852669, 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 01:50:27",
  "updated_at": "2026-10-21 01:50:27"
}