{
  "id": 2124,
  "curve_key": "185387040888036481:-78987171522012272194749121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3862230018500760",
    "91420337087883924609600"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 119.28366644243002,
  "faltings_height": 7.807402932807422,
  "conductor": "302411130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29",
    "127"
  ],
  "discriminant": "76663400156560832176235475416928253953600000000",
  "regulator": "119.838964065630546297150809186036083439282",
  "points": [
    [
      "26085120",
      "-91788817560"
    ],
    [
      "60079347737697720/2076481",
      "14726025084038870546430240/2992209121"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Rational 2-isogenous neighbor of curve#1779. The two submitted points are exact images of the two certified independent points on curve#1779 under the 2-isogeny. Since a nonzero isogeny has finite kernel, their images remain independent modulo torsion. The resulting model has full rational 2-torsion: x(x - 442050625)(x - 418079809).",
  "created_at": "2026-09-26 10:25:03",
  "updated_at": "2026-09-26 10:25:03"
}