{
  "id": 2768,
  "curve_key": "339393600:-3833227584000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-7070700",
    "4436606000"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 58.92801316134144,
  "faltings_height": 2.95079495062326,
  "conductor": "132033600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "53",
    "173"
  ],
  "discriminant": "14120625938457600000000",
  "regulator": "66.78138393338677327602095297217607635160535507",
  "points": [
    [
      "9305/4",
      "-192125/8"
    ],
    [
      "-10199/4",
      "-613899/8"
    ],
    [
      "40420",
      "-8109000"
    ],
    [
      "10045",
      "-973125"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1724 via the rational 2-torsion point x=5860. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:21:34",
  "updated_at": "2026-09-26 20:21:34"
}