{
  "id": 4589,
  "curve_key": "1702205783914128894542241:-2220829824576056355918929622980990961",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-35462620498211018636297",
    "2570404889564486437438128707183369"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 167.38190148545155,
  "faltings_height": 11.565042898707617,
  "conductor": "31530318364132052094720090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "37",
    "71",
    "199",
    "6229",
    "60133",
    "1787341"
  ],
  "discriminant": "36956888212049200929714493783423906963826670142242688301568000000",
  "regulator": "15994162.276478232068180408504337244172019564149461881302",
  "points": [
    [
      "14640832981264483/94249",
      "-823567921457363851825752/28934443"
    ],
    [
      "156318009127",
      "29096987433463036"
    ],
    [
      "52163700808457094114097/478298111281",
      "-47367281090654290490100079656494/330786669078938071"
    ],
    [
      "44738516786429767/408321",
      "121207709653150188657284/260917119"
    ],
    [
      "4106700030685865026052527/36901967940601",
      "-328145509176871381615595310067468236/224168347746800954099"
    ],
    [
      "764507765426317647/1038361",
      "-648444523465840997751748876/1058089859"
    ],
    [
      "21312444111899410498982583/194773648313689",
      "1025985769704514280383589437934487532/2718286940761069404637"
    ],
    [
      "8732035208354703/80089",
      "-2662850079489084047468/22665187"
    ],
    [
      "2711782888029279183/23785129",
      "-352834354780892473531991812/116000074133"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 495/97 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 14:18:07",
  "updated_at": "2026-10-18 14:18:07"
}