{
  "id": 6066,
  "curve_key": "538306672:-12493061818336",
  "ainvs": [
    "0",
    "1",
    "0",
    "-11214722",
    "14455824049"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 60.312389103207785,
  "faltings_height": 2.755689442257473,
  "conductor": "90040546876",
  "bad_primes": [
    "2",
    "7",
    "29",
    "59",
    "157",
    "11971"
  ],
  "discriminant": "-51664735998870981616",
  "regulator": "330.380013680947613505368674577775997813913291376",
  "points": [
    [
      "-1472",
      "166663"
    ],
    [
      "1370",
      "40803"
    ],
    [
      "1921",
      "2233"
    ],
    [
      "1950",
      "2407"
    ],
    [
      "2994",
      "87899"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own specialization at T=-2 of the X163 family printed by wgxli on curve#4645 and used by Maksym Voznyy on curve#5943 and curve#6012: y^2+(9*T^2-6*T+244)*x*y+(13*T-90)*(22*T-15)*(5*T+6)*(4*T+15)*y=x^3. At T=-2 the source model is [292,0,-191632,0,0]. Four points from exactly checked factor-product sections seeded a fresh point search, followed by the minimal-model change [u,r,s,t]=[2,-7104,-146,1133000]. All five listed rational points were checked exactly on the displayed global minimal model and returned as an independent set, with rank bounds [5,5]. The rational torsion subgroup is Z/3Z.",
  "created_at": "2026-10-28 19:46:20",
  "updated_at": "2026-10-28 19:46:20"
}