{
  "id": 1208,
  "curve_key": "4668159448660760425:5020847493645385711694076875",
  "ainvs": [
    "1",
    "0",
    "1",
    "-97253321847099176",
    "-5811166088712528801719002"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "naive_height": 128.96188963663366,
  "faltings_height": 8.797956061135562,
  "conductor": "122310700938581997673650",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "43",
    "47",
    "79",
    "89",
    "103",
    "199",
    "227",
    "313",
    "433"
  ],
  "discriminant": "44281411863251309409344858226580298292754182020250000",
  "regulator": "190927584.24006345525709277963872129983992782800085442271",
  "points": [
    [
      "-220901547",
      "-2211857309801"
    ],
    [
      "-173935998",
      "2417208096286"
    ],
    [
      "-62448798",
      "136581105886"
    ],
    [
      "-12148706363/81",
      "1694310408175519/729"
    ],
    [
      "-2073864385323/16129",
      "4378053471923781997/2048383"
    ],
    [
      "344461077",
      "1248963259411"
    ],
    [
      "-22312125534/121",
      "-3219724929585859/1331"
    ],
    [
      "-111103999263/1681",
      "-39467743884003169/68921"
    ],
    [
      "12544848026/25",
      "-1058759830411914/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve#1204, mapping all nine independent witness points to the global minimal model. The image curve has torsion Z/2Z. Isogenies preserve the Mordell-Weil rank, and all nine image points are independently certified by the site verifier. The conductor is 122310700938581997673650, unchanged by the isogeny. PARI/GP ellrank, supplied with these nine points, returns lower and upper bounds [9,9], proving that the rank is exactly 9.",
  "created_at": "2026-09-24 11:40:13",
  "updated_at": "2026-09-24 11:40:13"
}