{
  "id": 5347,
  "curve_key": "-2136848:-42605838424",
  "ainvs": [
    "0",
    "1",
    "1",
    "44518",
    "49327152"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 48.950514266075025,
  "faltings_height": 2.137831125192255,
  "conductor": "1056142691473638331",
  "bad_primes": [
    "1056142691473638331"
  ],
  "discriminant": "-1056142691473638331",
  "regulator": "235638.56167515540553625080987190810683820215506851138791",
  "points": [
    [
      "-315",
      "2036"
    ],
    [
      "-302",
      "2903"
    ],
    [
      "-294",
      "3303"
    ],
    [
      "-219",
      "5396"
    ],
    [
      "-37",
      "6901"
    ],
    [
      "172",
      "7880"
    ],
    [
      "255",
      "8793"
    ],
    [
      "507",
      "14229"
    ],
    [
      "783",
      "23766"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.1: https://johncremona.github.io/theses/womack.pdf. Nine supplied rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-21 15:17:08",
  "updated_at": "2026-10-21 15:17:08"
}