{
  "id": 2538,
  "curve_key": "393:-3429",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-8",
    "6"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 17.921428835607784,
  "faltings_height": -0.45127815670060784,
  "conductor": "238",
  "bad_primes": [
    "2",
    "7",
    "17"
  ],
  "discriminant": "28322",
  "regulator": "0.3209834542078720818983637322673382940906",
  "points": [
    [
      "-1",
      "4"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1808 via the rational 2-torsion point x=0. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:07:50",
  "updated_at": "2026-09-26 20:07:50"
}