{
  "id": 6360,
  "curve_key": "34290534404722900264281:-4688165612878202068476954112753245",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-714386133431727088839",
    "5426117607676515594095147180489"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 155.66746891225398,
  "faltings_height": 10.994136010871133,
  "conductor": "76991372034934662082752207026504149892549792743154890708806",
  "bad_primes": [
    "2",
    "3",
    "23",
    "37",
    "671647",
    "1406933179",
    "17554241580971",
    "303000518962990801080302879"
  ],
  "discriminant": "10614184531480162384052384765087915112486699527156819542897412772",
  "regulator": "311222932419488395.5357994252437171647964491465267835102096028004066273766345",
  "points": [
    [
      "5770345780",
      "1223106745416223"
    ],
    [
      "6451958485",
      "-1041880649349362"
    ],
    [
      "-16289871920",
      "3569419440402547"
    ],
    [
      "25132188001",
      "-1829273710174850"
    ],
    [
      "26841619784",
      "2364196163188653"
    ],
    [
      "7604128282",
      "-658430368573637"
    ],
    [
      "1616011273",
      "2067819726757342"
    ],
    [
      "186342519298",
      "79641456933414967"
    ],
    [
      "29628447628",
      "3204536226669655"
    ],
    [
      "-18701336222",
      "-3499346017178033"
    ],
    [
      "-20000921414",
      "3422493422430019"
    ],
    [
      "-28296522917",
      "1727418982085167"
    ],
    [
      "46189319650",
      "-8424503033835617"
    ],
    [
      "5504128232",
      "-1288720968124245"
    ],
    [
      "21897041332",
      "531381064375213"
    ],
    [
      "33074555347/4",
      "2324744455335461/8"
    ],
    [
      "87005744077",
      "-24533772527882747"
    ],
    [
      "-3459581480",
      "-2802887482736357"
    ],
    [
      "30125997568",
      "-3353542594915235"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From the Layr-Labs elliptic-rank-challenge-public repository, submission/board/1-19-m10-kh-b2.ec. The source credits its “kshitij-hash lane” with this find using Mestre's ten-root construction, with roots [0,7,38,64,65,73,75,86,105,125].\r\n\r\nThe displayed model and all 19 rational points are reproduced from that source. All points were checked exactly on this model, which was independently confirmed minimal. The minimal discriminant was fully factored and every bad-reduction prime proved prime. The source describes the rank as certified 19; no matching upper-bound certificate is asserted here.\r\n\r\nSource at commit 140b9d566eeaefe70e423bca75e3c5f091b0eaab:\r\nhttps://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/140b9d566eeaefe70e423bca75e3c5f091b0eaab/submission/board/1-19-m10-kh-b2.ec",
  "created_at": "2026-11-01 14:02:54",
  "updated_at": "2026-11-01 14:02:54"
}