{
  "id": 4728,
  "curve_key": "881587894524219741316800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-18366414469254577944100",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 165.40803497976833,
  "faltings_height": 11.852243326622185,
  "conductor": "293862631508073247105600",
  "bad_primes": [
    "2",
    "5",
    "23",
    "41",
    "127",
    "113161"
  ],
  "discriminant": "396509060811465164039447214329498950068472138802912426615239744000000",
  "regulator": "29393654.474476138793587885824135906355079360350232",
  "points": [
    [
      "4588738260533260/9801",
      "297535003425944535708100/970299"
    ],
    [
      "-2436661497635/81",
      "16707945924712689625/729"
    ],
    [
      "-96349391915974915/734449",
      "7753343677163842423079625/629422793"
    ],
    [
      "894562865423252035340/1604563249",
      "25953161405852169243810589139100/64273990065193"
    ],
    [
      "3731434741025281/2116",
      "227262338335460096407521/97336"
    ],
    [
      "392870515101972767209657260/733713640948201",
      "7533528587070739065115545543747395466900/19874210715696421768949"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 135522745210. Source: Watkins et al. electronic data http://magma.maths.usyd.edu.au/~watkins/PTS.r6r7 (paper Sec. 15); Watkins, Donnelly, Elkies, Fisher, Granville, Rogers, 'Ranks of quadratic twists of elliptic curves', Publ. Math. Besancon 2014/2, 63-98, doi:10.5802/pmb.9 (https://pmb.centre-mersenne.org/item/10.5802/pmb.9.pdf).",
  "created_at": "2026-10-20 21:26:25",
  "updated_at": "2026-10-20 21:26:25"
}