{
  "id": 4726,
  "curve_key": "739811067192126749437632:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-15412730566502640613284",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 164.88204537560887,
  "faltings_height": 11.808410859608895,
  "conductor": "246603689064042249812544",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "41",
    "751",
    "5647"
  ],
  "discriminant": "234325058113846545520368187605974516981426632957152094385667666579456",
  "regulator": "19601741.275631068224865671682162798833186232181234",
  "points": [
    [
      "15630483860187756/105625",
      "1063478409088682202316596/34328125"
    ],
    [
      "-28276242435587762/346921",
      "5462956723015935950708440/204336469"
    ],
    [
      "-89890066408315782/786769",
      "11457315952350802921094400/697864103"
    ],
    [
      "-352286054891120532/4583881",
      "265269359080039106910974220/9814089221"
    ],
    [
      "-151105201632378829542/59064066961",
      "90117807456685802222515310970480/14354399257598791"
    ],
    [
      "-170088198869948570617350/2309843713489",
      "95216429170143567217978852044143520/3510539743103711513"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 124148018778. 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 21:26:17",
  "updated_at": "2026-10-20 21:26:17"
}