{
  "id": 5316,
  "curve_key": "616656863040:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-12847017980",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 81.44273570535398,
  "faltings_height": 4.8551350537543225,
  "conductor": "330091741956886560800",
  "bad_primes": [
    "2",
    "5",
    "17",
    "29",
    "43",
    "157",
    "193"
  ],
  "discriminant": "135702225407028545005374821888000",
  "regulator": "173857.6851826904336458515973702319123792859937188530",
  "points": [
    [
      "-112230",
      "5312220"
    ],
    [
      "-108016",
      "11287672"
    ],
    [
      "119306",
      "12863356"
    ],
    [
      "-978895/16",
      "1510434985/64"
    ],
    [
      "-311750/9",
      "542320300/27"
    ],
    [
      "878729/4",
      "705619387/8"
    ],
    [
      "3787625/16",
      "6471536075/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5315: https://elliptic-rank.icarm.cloud/curve/5315. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (2,16,19,22), 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.",
  "created_at": "2026-10-21 13:07:03",
  "updated_at": "2026-10-21 13:07:03"
}