{
  "id": 2592,
  "curve_key": "1578681552280561:5103483899633600677559",
  "ainvs": [
    "1",
    "0",
    "0",
    "-32889199005845",
    "-5906812809786954975"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 104.9860992990348,
  "faltings_height": 6.816678665009829,
  "conductor": "40682217030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "167",
    "181"
  ],
  "discriminant": "2261805885819848354828861651782100769000000",
  "regulator": "111.49324729911060906355474814191521247455169",
  "points": [
    [
      "-910910",
      "4827095455"
    ],
    [
      "6602050",
      "8041637695"
    ],
    [
      "-185690",
      "440524255"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [
    {
      "kind": "rank_improved",
      "user": "Tom Fisher",
      "old_rank": 2,
      "new_rank": 3,
      "at": "2026-09-27 14:01:22"
    }
  ],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-7, q=58; A=(3q-p)(p+q)^3=24009831, B=-(p+3q)(p-q)^3=45862375. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 20:11:27",
  "updated_at": "2026-09-27 14:01:22"
}