{
  "id": 6243,
  "curve_key": "3121196290119519696:-6116861428129152895722966720",
  "ainvs": [
    "0",
    "0",
    "0",
    "-65024922710823327",
    "7079700727001334370049730"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 127.96169327455164,
  "faltings_height": 8.635271673242793,
  "conductor": "1565026656631732554825730389590162771004061273464",
  "bad_primes": [
    "2",
    "3",
    "829804376761",
    "26194705584648815644332131433822767"
  ],
  "discriminant": "-4056549093989450782108293169817701902442526820818688",
  "regulator": "394054020067529.922096777908420886666945314278552000522055816136279969900",
  "points": [
    [
      "191376615",
      "1282427904600"
    ],
    [
      "436842813",
      "-7876386381474"
    ],
    [
      "-121504335",
      "3631350348630"
    ],
    [
      "211297923",
      "-1665487410624"
    ],
    [
      "79648743",
      "1551074725224"
    ],
    [
      "127619097",
      "927234771822"
    ],
    [
      "453351165",
      "8412883426530"
    ],
    [
      "619761813",
      "14311993746474"
    ],
    [
      "116567457",
      "-1041069733722"
    ],
    [
      "2409776989/49",
      "686066542627906/343"
    ],
    [
      "-274542351",
      "2058780538134"
    ],
    [
      "-275652399",
      "-2014630791498"
    ],
    [
      "-189019331",
      "-3552087743326"
    ],
    [
      "331537629",
      "4686489060606"
    ],
    [
      "251722998",
      "-2581031967876"
    ],
    [
      "1149397869",
      "-38089729442574"
    ],
    [
      "278274033",
      "3245535855126"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original search by i34-9 (2026), public Yukon elliptic-rank challenge submission b93c15c3-3f2a-4c98-bd8d-34fd1f74a78a, validated 2026-10-31. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/15252c70964f8ce1651ce8e37faebdb371067b45/submission/board/1-17-mestre.ec . Mestre ten-root construction with roots [0, 13, 17, 25, 33, 41, 49, 56, 69, 77]. The seventeen supplied points were checked exactly on the displayed global minimal model and certified independent modulo torsion by an exact rank-17 F_2 reduction matrix at 19 good primes. The rational torsion subgroup is trivial (the gcd of #E(F_p) over good primes p >= 5 is 1). The complete bad-prime list was verified from the minimal discriminant, with every large factor proved prime.",
  "created_at": "2026-10-31 20:39:35",
  "updated_at": "2026-10-31 20:39:35"
}