{
  "id": 4723,
  "curve_key": "213146087445443743174848:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-4440543488446744649476",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 161.14879422013092,
  "faltings_height": 11.497306596652402,
  "conductor": "71048695815147914391616",
  "bad_primes": [
    "2",
    "11",
    "41",
    "73",
    "83",
    "89",
    "137"
  ],
  "discriminant": "5603873937673552989300498033450919374305569702372133792442324619264",
  "regulator": "3563463.7864788079532444667284295752395634886940862",
  "points": [
    [
      "9545443187049/100",
      "21115589873934251157/1000"
    ],
    [
      "73145926991313/784",
      "437846569428939872487/21952"
    ],
    [
      "-107791645753616/2025",
      "842818572202479027848/91125"
    ],
    [
      "443592838138329/2704",
      "8537296635485843022435/140608"
    ],
    [
      "4279322629593/64",
      "728847146421825123/512"
    ],
    [
      "22114530754212226/140625",
      "2978793707011327140698224/52734375"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 66637403074. 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 21:26:05",
  "updated_at": "2026-10-20 21:26:05"
}