{
  "id": 4587,
  "curve_key": "81995195301441140331601:-23479003150222948839978656564957401",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1708233235446690423575",
    "27174772164467541721095480155625"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 158.28284281361297,
  "faltings_height": 10.80809937662565,
  "conductor": "234766387614235234999569510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "29",
    "61",
    "11597",
    "763393287049"
  ],
  "discriminant": "4338177848470813268550996353486882523154086900977020416000000",
  "regulator": "823615269.42082442897917752844036022307725508998220643901",
  "points": [
    [
      "75634748002958950/3193369",
      "-259228293704427321148225/5706550403"
    ],
    [
      "264264400357750/5041",
      "3234910150133966639075/357911"
    ],
    [
      "33891375856",
      "-2865133215287603"
    ],
    [
      "-285029425333250/11881",
      "9547159897948794478825/1295029"
    ],
    [
      "16128853798486/112225",
      "-195095258785051524985189/37595375"
    ],
    [
      "-32393084750",
      "-6965560990166675"
    ],
    [
      "18995244589750/841",
      "-8244521178543419575/24389"
    ],
    [
      "64410348995098999750/2661218569",
      "12413846382336263983832129975/137284282319003"
    ],
    [
      "284743063488286/11881",
      "-31456169691399687767/1295029"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 73/83 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": "2026-10-18 13:41:20",
  "updated_at": "2026-10-18 13:41:20"
}