{
  "id": 5091,
  "curve_key": "218537106560540453274831184669031041:-102584521701174775825118032036575575324213496585908161",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4552856386677926109892316347271480",
    "118732085302285619788555986337690851171257777294400"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 244.12505360688013,
  "faltings_height": 18.171641679573845,
  "conductor": "12586515643015858148783450187219322636466538690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "53",
    "61",
    "97",
    "433",
    "509",
    "821",
    "953",
    "2109979",
    "44950014478843"
  ],
  "discriminant": "-50108167234921189007404640083842306287894406653040397911321447775855739386831760747912581632000000000",
  "regulator": "549841813752594.01099186510890041379890114296197122511952195756",
  "points": [
    [
      "178341872994466086207670/5480281",
      "-28783992553130306250163635358126130/12829337821"
    ],
    [
      "9110132810087690877335785485040/230805766597849",
      "2529821588904363922202479808265818588366627240/3506468832244135177757"
    ],
    [
      "-912538875437308105865626025095040/30405772592445121",
      "80117079501092792360213625239547931535089322760520/5301930915839635378468831"
    ],
    [
      "-261154018133034767617178910/3362028289",
      "-374787388971973684343937977780063572410/194940486281087"
    ],
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      "-87919780026226668560/1849",
      "-1199765482359540565040191966760/79507"
    ],
    [
      "7360850493699308041217440/161366209",
      "5007360911899749942588329559787713640/2049834952927"
    ],
    [
      "26466011441881141886910987835/567150572836",
      "1199853996514005972009911232818528409360505/427117693499354584"
    ],
    [
      "876167296340788450785570698245360/342897843285001",
      "25925708164868923052303120994706298167058286617320/6349611155927849302501"
    ],
    [
      "46747289048240350555208560/1248986281",
      "38453368401588045199299002392411769320/44140424156821"
    ],
    [
      "35534127212488480",
      "-1348455731997431521128680"
    ],
    [
      "87017974816973229421855160944/2607885861025",
      "8387047538316015593500681780462465624347832/4211461837539967375"
    ],
    [
      "1051564996885618702059825014512/27262506265201",
      "101328079071660727729017959880968873621090296/142347114350313506551"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 8945/2479 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-10-21 02:32:34",
  "updated_at": "2026-10-21 02:32:34"
}