{
  "id": 3334,
  "curve_key": "114540502194337210948576:-38764896077738205124818546567641824",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2386260462382025228095",
    "44866777866957132073671901969850"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 159.28564633282835,
  "faltings_height": 10.69332572766621,
  "conductor": "1185557421935264818440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "31",
    "67",
    "89",
    "193",
    "347",
    "2039"
  ],
  "discriminant": "1339963598635962003158421351517155890816106884858381250000",
  "regulator": "7534307.037734179442494821425851534602589587876112350",
  "points": [
    [
      "708096349979/25",
      "-4390220390578083/125"
    ],
    [
      "12478492695610/441",
      "-249868351726662500/9261"
    ],
    [
      "30449171435",
      "-661917974787225"
    ],
    [
      "53672162954",
      "-8450116866863100"
    ],
    [
      "130631164792874/3481",
      "-586887323235576456600/205379"
    ],
    [
      "27136418855435/961",
      "-298924064887865625/29791"
    ],
    [
      "658848929570435/22801",
      "-696275010485001128025/3442951"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1830 (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 7 carries over. Torsion ℤ/4ℤ.",
  "created_at": "2026-09-26 21:01:32",
  "updated_at": "2026-09-26 21:01:32"
}