{
  "id": 5235,
  "curve_key": "9029601648:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-188116701",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 68.77132226734957,
  "faltings_height": 3.7991839339206224,
  "conductor": "1132412582243948832",
  "bad_primes": [
    "2",
    "3",
    "19",
    "23",
    "43",
    "47",
    "71"
  ],
  "discriminant": "426051438285245662977286464",
  "regulator": "15081.306864827138322561402483971274886624357712509",
  "points": [
    [
      "-12212",
      "689978"
    ],
    [
      "-6063",
      "957954"
    ],
    [
      "-4047",
      "833682"
    ],
    [
      "-3053",
      "738826"
    ],
    [
      "210657",
      "96480906"
    ],
    [
      "-76751/100",
      "379380193/1000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of the Aguirre–Castaneda–Peral curve at tuple (4,7,11,13), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 10:47:20",
  "updated_at": "2026-10-21 10:47:20"
}