{
  "id": 72,
  "curve_key": "336:-31320",
  "ainvs": [
    "0",
    "0",
    "1",
    "-7",
    "36"
  ],
  "rank_lower_bound": 4,
  "naive_height": 20.70402430020948,
  "faltings_height": -0.2176951115207691,
  "conductor": "545723",
  "bad_primes": [
    "545723"
  ],
  "discriminant": "-545723",
  "regulator": "3.306378474591305516092927336098302768950667315",
  "points": [
    [
      "-4",
      "0"
    ],
    [
      "-3",
      "5"
    ],
    [
      "-2",
      "6"
    ],
    [
      "-1",
      "6"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=336, c6=-31320, Delta=-545723 with 545723 prime. The submitted points (-4,0), (-3,5), (-2,6), and (-1,6) 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": "2026-06-01 13:36:55",
  "updated_at": "2026-07-01 23:03:09"
}