{
  "id": 1162,
  "curve_key": "-2233164665901811199:-11655710172290411898384823201",
  "ainvs": [
    "1",
    "0",
    "0",
    "46524263872954400",
    "13490405295879813538469375"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 129.25118742862816,
  "faltings_height": 8.83777782138536,
  "conductor": "965575150587952905",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "137",
    "173",
    "347",
    "617"
  ],
  "discriminant": "-85065061547688494796290171100936035530110547655859375",
  "regulator": "276991.02745939693646544486082098299243157800924115",
  "points": [
    [
      "532637450",
      "13761333456275"
    ],
    [
      "233764106",
      "6094167446387"
    ],
    [
      "10876343075",
      "1134514175511275"
    ],
    [
      "881912531",
      "27210688978667"
    ],
    [
      "421169675",
      "10382165439050"
    ],
    [
      "-108836989621/625",
      "5137022971960067/15625"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1112 and mapping all 6 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:38:00",
  "updated_at": "2026-09-23 21:38:00"
}