{
  "id": 6375,
  "curve_key": "10932560253152922233162734801:-1148315876942459974819964771809711094242201",
  "ainvs": [
    "1",
    "0",
    "0",
    "-227761671940685879857556975",
    "1329069302016717101828223428734214525625"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 193.6937406398608,
  "faltings_height": 13.973004766522902,
  "conductor": "1459962723141988049841475349454286290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "31",
    "41",
    "43",
    "47",
    "53",
    "137",
    "3184179307",
    "391512351343"
  ],
  "discriminant": "-6921412109743309825444413417903120358110920795030340763647188995356283392000000",
  "regulator": "202628527.765566109359252618061301221901130176501782657724658",
  "points": [
    [
      "-3111976384550",
      "44807597246709487525"
    ],
    [
      "-10888868692970",
      "50180387293201180045"
    ],
    [
      "9438714134950",
      "-4492293256698721475"
    ],
    [
      "8304179822710",
      "3216624604629259165"
    ],
    [
      "13250620652950",
      "25251049160775712525"
    ],
    [
      "12868043211550",
      "22999927636790547925"
    ],
    [
      "-16832872762298",
      "19835129337022642621"
    ],
    [
      "189484574050",
      "-35859709825229252075"
    ],
    [
      "5926469897350",
      "13689492316665872125"
    ],
    [
      "-11640117660218",
      "49021380670253081341"
    ],
    [
      "8176304569750",
      "-3663671603883180275"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/3 K3 family y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3 (Layr-Labs 3-r12-z3k3), rational parameter search. Here t=793/323. An integral model is [1,0,0,a4,a6] as above. 11 points obtained by specializing 17 polynomial sections at t; PARI/GP 2.19 ellrank bounds [11,11]; Neron-Tate regulator nonzero.",
  "created_at": "2026-11-01 20:31:49",
  "updated_at": "2026-11-01 20:31:49"
}