{
  "id": 69,
  "curve_key": "1:-865",
  "ainvs": [
    "1",
    "0",
    "0",
    "0",
    "1"
  ],
  "rank_lower_bound": 2,
  "naive_height": 13.525459013863758,
  "faltings_height": -0.8152203271973504,
  "conductor": "433",
  "bad_primes": [
    "433"
  ],
  "discriminant": "-433",
  "regulator": "0.224694163418166741612071133995500441366829",
  "points": [
    [
      "0",
      "1"
    ],
    [
      "-1",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=1, c6=-865, Delta=-433. The submitted points (0,1), (-1,1) were checked exactly on the curve, with an additional finite-field independence sanity check; the site Neron-Tate verifier gives the definitive certificate.",
  "created_at": "2026-05-29 13:46:04",
  "updated_at": "2026-07-01 23:04:07"
}