{
  "id": 4581,
  "curve_key": "10758025213021947942902719919281:-35468164472381173729280861804519698103702761321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-224125525271290582143806664985",
    "41051116287478191657688706332867805265767225"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 214.3699294068878,
  "faltings_height": 15.701096040381813,
  "conductor": "558341382311826958196586943618604792370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "31",
    "41",
    "89",
    "127",
    "131",
    "151",
    "3680055649",
    "396687343189"
  ],
  "discriminant": "-7470773989038667208039204073219966949534207294785627321767176636964985159878832192000000",
  "regulator": "2969106036.2403860837557744132828092496778257113810701615672556",
  "points": [
    [
      "-481540726620070",
      "6108708152925451520915"
    ],
    [
      "-371095610684734",
      "8550954163440364202267"
    ],
    [
      "603897836829170",
      "11222266270865219635715"
    ],
    [
      "-144411766233670",
      "8390816884653664020755"
    ],
    [
      "282869883217070",
      "-535438028240542973785"
    ],
    [
      "61987569235580690",
      "15432784073594826300252995"
    ],
    [
      "278169210334970",
      "480107708678693831315"
    ],
    [
      "308040368860250",
      "-1114005976467492637165"
    ],
    [
      "952696519654490",
      "26310151137416798834195"
    ],
    [
      "-336150412004101630/841",
      "-199300298327616701823394865/24389"
    ],
    [
      "300559170957110",
      "-916183516103561185285"
    ],
    [
      "-500934739918834",
      "-5255569331843048866453"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-r12-z3k3.ec.\r\n\r\nThe original submission describes a K3 family with Z/3Z torsion and generic rank at least 5, specialized at t = 2417/727. The submitter reports Mestre–Nagao sieving, PARI/GP rank calculations and saturation checks.\r\n\r\nSubmitted to ICARM to document these improvements and make the curve available to other researchers.",
  "created_at": "2026-10-18 08:11:41",
  "updated_at": "2026-10-18 08:11:41"
}