{
  "id": 3349,
  "curve_key": "72036103740489:-611399823976126993797",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-1500752161260",
    "707639060345594706"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6
  ],
  "naive_height": 95.72456565031585,
  "faltings_height": 5.467141525594601,
  "conductor": "4149942570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "37",
    "107",
    "613"
  ],
  "discriminant": "12854631399414927145471138934070",
  "regulator": "3736.096197131434867365898516495908508096572721",
  "points": [
    [
      "749415",
      "61601421"
    ],
    [
      "19361095/4",
      "-82711160373/8"
    ],
    [
      "708517",
      "1436030"
    ],
    [
      "9683402665/13689",
      "-521482247623/1601613"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1612 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 4 carries over. Torsion ℤ/6ℤ.",
  "created_at": "2026-09-26 21:09:25",
  "updated_at": "2026-09-26 21:09:25"
}