{
  "id": 2637,
  "curve_key": "2079507361:70358555081359",
  "ainvs": [
    "1",
    "1",
    "1",
    "-43323070",
    "-81451564105"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 64.36619057080259,
  "faltings_height": 3.3850171579250348,
  "conductor": "308490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "113"
  ],
  "discriminant": "2339232164953982451562500",
  "regulator": "5.34385037846615349708486300991640982157832",
  "points": [
    [
      "80173",
      "-22662687"
    ],
    [
      "12373",
      "-1136187"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2068 via the rational 2-torsion point x=2641. 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 20:14:24",
  "updated_at": "2026-09-26 20:14:24"
}