{
  "id": 5240,
  "curve_key": "249539509296:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5198739777",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 78.72864928047935,
  "faltings_height": 4.628961185014769,
  "conductor": "96095627622976034592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "67",
    "71",
    "83"
  ],
  "discriminant": "8992370910948218462720850587712",
  "regulator": "69983.72045484524083168729880760855776878890254742469",
  "points": [
    [
      "-64823",
      "8038052"
    ],
    [
      "-50049",
      "11611368"
    ],
    [
      "-46431",
      "11886336"
    ],
    [
      "-16929",
      "9119088"
    ],
    [
      "-5561",
      "5360804"
    ],
    [
      "-4473",
      "4812948"
    ],
    [
      "-1988",
      "3213602"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,15,16,18), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 10:54:04",
  "updated_at": "2026-10-21 10:54:04"
}