{
  "id": 5054,
  "curve_key": "6689531657892809324718247779076800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-139365242872766860931630162064100",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 233.65755580259713,
  "faltings_height": 17.53970339519125,
  "conductor": "2229843885964269774906082593025600",
  "bad_primes": [
    "2",
    "5",
    "11",
    "17",
    "43",
    "193",
    "409",
    "1193",
    "1559"
  ],
  "discriminant": "173238096009020285000252496373565722232373011364077623604839208447358841233505580751682222144000000",
  "regulator": "1456072155.091865677573843379580969752708624418007809",
  "points": [
    [
      "3551109721579398321765/219961",
      "144347200380223074305917559445075/103161709"
    ],
    [
      "75398094273297634565/6241",
      "139090003900240897824954102525/493039"
    ],
    [
      "4120565424257133841/324",
      "3111178132571593217692998439/5832"
    ],
    [
      "132426550038117209106529/583696",
      "48125345606832471814431676379324433/445943744"
    ],
    [
      "387097181553305641/4",
      "239042071682596306748359989/8"
    ],
    [
      "36396443980054413043569/4900",
      "6943650973367825308600005891643497/343000"
    ],
    [
      "613176294234149213628622969/49260914704",
      "4814119004880986781631038196865693098803/10933361496723392"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 11805305708568790, 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 01:50:23",
  "updated_at": "2026-10-21 01:50:23"
}