{
  "id": 5247,
  "curve_key": "-270890785108944:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "5643558023103",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 99.69821054580314,
  "faltings_height": 6.376424623791752,
  "conductor": "113243545458240858601772832",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "37",
    "43",
    "53"
  ],
  "discriminant": "-11503737351638720895791563856874247278528",
  "regulator": "16211921.6160584152378015493148246600713726769035597296",
  "points": [
    [
      "757575",
      "2170300860"
    ],
    [
      "2026332",
      "4444759242"
    ],
    [
      "3867721",
      "8926700068"
    ],
    [
      "6084351",
      "16111361448"
    ],
    [
      "53535559/25",
      "585036588752/125"
    ],
    [
      "108971632/9",
      "1159237744588/27"
    ],
    [
      "481820031/259081",
      "13509977340983508/131872229"
    ],
    [
      "976200316/729",
      "62113802153858/19683"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (2,14,18,22), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Selected in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C2.",
  "created_at": "2026-10-21 11:03:33",
  "updated_at": "2026-10-21 11:03:33"
}