{
  "id": 6040,
  "curve_key": "240100016800:-117649012348000216",
  "ainvs": [
    "0",
    "1",
    "1",
    "-5002083683",
    "136166171004513"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 78.61296423043339,
  "faltings_height": 3.593714543203521,
  "conductor": "343000027",
  "bad_primes": [
    "19",
    "31",
    "37",
    "15739"
  ],
  "discriminant": "-343000027",
  "regulator": "2252.8841038424004949292614567469570113296899",
  "points": [
    [
      "1043029/25",
      "38997483/125"
    ],
    [
      "175642175269/4301476",
      "-4181909557/8921261224"
    ],
    [
      "1448993722527/35485849",
      "-104893754993/211389202493"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The specialization a=700, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+700*x*y-y=x^3, with discriminant -343000027. The displayed equation is its global minimal model. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/3Z.",
  "created_at": "2026-10-28 15:54:46",
  "updated_at": "2026-10-28 15:54:46"
}