{
  "id": 5059,
  "curve_key": "147442589214440927890062576904427712:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3071720608634185997709637018842244",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 242.9362408294518,
  "faltings_height": 18.312927147429143,
  "conductor": "49147529738146975963354192301475904",
  "bad_primes": [
    "2",
    "17",
    "53",
    "71",
    "89",
    "107",
    "257",
    "263",
    "673"
  ],
  "discriminant": "1854919677708369531988260618970144010828377918910916163113353941368937956098372916347518956479645618176",
  "regulator": "7698895067.712369699654952226091074907501519576194987",
  "points": [
    [
      "5864898372882946609/100",
      "4645622717581500679939035273/1000"
    ],
    [
      "46809198933785611636532725/485276841",
      "262113124439040583564309666013100067285/10690163530389"
    ],
    [
      "-192202903710627563983289507/24061904161",
      "18295434730756403062806467049806634610665/3732458511550159"
    ],
    [
      "-2829102178332175820766261054703/1018406635050256",
      "94817863428382630503657152722960713114048873465/32499885446535133795904"
    ],
    [
      "-3462905263918763240068518/67782289",
      "2710209359398387466642295711962606280/558051585337"
    ],
    [
      "1682459725372701456023969/30250000",
      "182768181825209591427596211644140047/166375000000"
    ],
    [
      "-580434783190475821953899122718/16510967630161",
      "538978704596838618632881923274496511430946160/67090154028399672409"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 55423105368015838, 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 01:50:42",
  "updated_at": "2026-10-21 01:50:42"
}