{
  "id": 6241,
  "curve_key": "5292789127977936:-424959887645541068472000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-110266440166207",
    "491851721811968829250"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 108.81256347066925,
  "faltings_height": 7.037150850135353,
  "conductor": "83500588833121557508864755335066677535752",
  "bad_primes": [
    "2",
    "7",
    "1291",
    "1154982140548876251920780614903544837"
  ],
  "discriminant": "-18704131898619228881985705195054935768008448",
  "regulator": "5411936736791.754730229369335992392472742232368833238487399865983495057",
  "points": [
    [
      "4043439",
      "10587912664"
    ],
    [
      "11105501",
      "-25237927862"
    ],
    [
      "17197867",
      "-60679974488"
    ],
    [
      "4235561",
      "-10039788598"
    ],
    [
      "18400817",
      "-68506882738"
    ],
    [
      "25868858",
      "122273333434"
    ],
    [
      "-749258",
      "23959321988"
    ],
    [
      "31659167",
      "169508057488"
    ],
    [
      "9095521",
      "15536403358"
    ],
    [
      "2320437",
      "-15763236338"
    ],
    [
      "9738107",
      "18480722512"
    ],
    [
      "5253193",
      "7587366934"
    ],
    [
      "-5442971",
      "-30508616194"
    ],
    [
      "779377453/169",
      "-19823776352086/2197"
    ],
    [
      "55894175",
      "411036347120"
    ],
    [
      "56749381/9",
      "-185631668558/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original search by i34-9 (2026), public Yukon elliptic-rank challenge submission 5ff5d484-4937-489f-9836-0cd5cfd29e10, validated 2026-10-31. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/f5f6b67ffb7690c5bab6721024cb2539fbe64e8b/submission/board/1-16-mestre-10311649.ec . Mestre ten-root construction with roots [0, 6, 18, 28, 38, 40, 119, 127, 130, 132]. The sixteen supplied points were checked exactly on the displayed global minimal model and certified independent modulo torsion by an exact rank-16 F_2 reduction matrix at 26 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 20:37:27",
  "updated_at": "2026-10-31 20:37:27"
}