{
  "id": 6240,
  "curve_key": "142504788299355001:-53018766584899021056897485",
  "ainvs": [
    "1",
    "1",
    "0",
    "-2968849756236562",
    "61364311939945727791360"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 118.49445598846677,
  "faltings_height": 7.755897529215454,
  "conductor": "7999876719625417442633368343888625578394499782",
  "bad_primes": [
    "2",
    "3",
    "1567",
    "561313",
    "4437379",
    "341610666946925529805004012533"
  ],
  "discriminant": "47999260317752504655800210063331753470366998692",
  "regulator": "4662425823827369673.09716522944044686963625787068331948466977945061441868",
  "points": [
    [
      "27834502",
      "17100501442"
    ],
    [
      "7708809",
      "197318516207"
    ],
    [
      "-62814014",
      "-3238317716"
    ],
    [
      "415075933/16",
      "2718090753883/64"
    ],
    [
      "1665672381/169",
      "399460417270123/2197"
    ],
    [
      "1791230711",
      "75774565929530"
    ],
    [
      "9410266243/169",
      "575763879478462/2197"
    ],
    [
      "8163498976",
      "737568670758424"
    ],
    [
      "4857573174/289",
      "-625592678575768/4913"
    ],
    [
      "375693890566/7225",
      "-133985022480188294/614125"
    ],
    [
      "5518219534/121",
      "192022960478672/1331"
    ],
    [
      "421514651/4",
      "7667508165901/8"
    ],
    [
      "500652410530/6561",
      "-280801404206172980/531441"
    ],
    [
      "-418144353870/8281",
      "216504757844842550/753571"
    ],
    [
      "-181517285095/3136",
      "-34802885309763425/175616"
    ],
    [
      "1180784159234/34225",
      "10862573204305378/6331625"
    ],
    [
      "3452819206/225",
      "-470334684932066/3375"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original search by i34-9 (2026), public Yukon elliptic-rank challenge submission 7ab99cc9-db1a-4085-aaf6-bae4d565783e, validated 2026-10-31. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/0b63ff3577c4e70ecc2a8df8e5bc7ef3ada5ae89/submission/board/1-17-mestre-10311116.ec . Mestre ten-root construction with roots [0, 8, 13, 32, 50, 53, 54, 63, 76, 103]. 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 24 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 20:36:24",
  "updated_at": "2026-10-31 20:36:24"
}