{
  "id": 2570,
  "curve_key": "32656:5120704",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-680",
    "-5700"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 31.181351655148877,
  "faltings_height": 0.5863414834987034,
  "conductor": "840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7"
  ],
  "discriminant": "4978713600",
  "regulator": "2.196597963753069286457897954426581558085",
  "points": [
    [
      "-15",
      "-30"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1167 via the rational 2-torsion point x=10. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny.",
  "created_at": "2026-09-26 20:09:56",
  "updated_at": "2026-09-26 20:09:56"
}