{
  "id": 3351,
  "curve_key": "5640342328849081:-423599187500438313319021",
  "ainvs": [
    "1",
    "0",
    "1",
    "-117507131851023",
    "490276827592505578756"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 108.8061634655494,
  "faltings_height": 6.686144358070699,
  "conductor": "57274747140390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "43",
    "61",
    "149",
    "19777"
  ],
  "discriminant": "1471274953921175179720304178694125843750",
  "regulator": "48589.2882074758600329220050948485150796139586163",
  "points": [
    [
      "17511370",
      "-61672310698"
    ],
    [
      "6276670",
      "-55286473"
    ],
    [
      "8396420",
      "9772515027"
    ],
    [
      "87198258296/7225",
      "-17697021500106849/614125"
    ],
    [
      "18190377830/49",
      "-2452396608802239/343"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1673 (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 5 carries over. Torsion ℤ/6ℤ.",
  "created_at": "2026-09-26 21:10:14",
  "updated_at": "2026-09-26 21:10:14"
}