{
  "id": 5090,
  "curve_key": "2075714821407726576:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-43244058779327637",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 126.53051178148903,
  "faltings_height": 8.612449726765576,
  "conductor": "135695137938136502727507141369888",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "23",
    "31",
    "43",
    "47",
    "107",
    "179"
  ],
  "discriminant": "5175583515579988446147720786121303391752754551286592",
  "regulator": "1298534027.8731865815221134486102816730846476361031382415",
  "points": [
    [
      "-143692500",
      "1801929814650"
    ],
    [
      "-18559257",
      "892291958046"
    ],
    [
      "-14360409",
      "786155803902"
    ],
    [
      "270538800",
      "2846379295620"
    ],
    [
      "527366448",
      "11129386748004"
    ],
    [
      "702885568",
      "17800664870296"
    ],
    [
      "-1465457491977/66049",
      "16532173097887842954/16974593"
    ],
    [
      "-128485736211/625",
      "7020717598041462/15625"
    ],
    [
      "-128485736211/961",
      "54865208162403954/29791"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5089: https://elliptic-rank.icarm.cloud/curve/5089. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (9,27,29,41), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Nine rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion C2.",
  "created_at": "2026-10-21 02:32:30",
  "updated_at": "2026-10-21 02:32:30"
}