{
  "id": 2920,
  "curve_key": "421225351640075423419681:-275447407313468420317987302705775921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-8775528159168237987910",
    "318804869575042340614036099040100"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 163.20740956025853,
  "faltings_height": 11.453278315516393,
  "conductor": "2258228975265200784470",
  "bad_primes": [
    "2",
    "5",
    "13",
    "29",
    "37",
    "43",
    "73",
    "97",
    "163",
    "211",
    "277",
    "5581"
  ],
  "discriminant": "-655627543267378610060412595544576918156889807797205950381656000000",
  "regulator": "508395.0135300124070219387019938532602770121622266179",
  "points": [
    [
      "35287239459367480/66049",
      "-6533016899715065403394530/16974593"
    ],
    [
      "-23093969804641034/491401",
      "8628490913898384567135942/344472101"
    ],
    [
      "-8917792479425504/119025",
      "-968012976517033138859066/41063625"
    ],
    [
      "1463321465020",
      "-1766608171934182710"
    ],
    [
      "35126328981723772",
      "-6583383396938297894753718"
    ],
    [
      "-85538665784",
      "-21061227650166678"
    ],
    [
      "3986889920",
      "-16848775764582710"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1266 via the rational 2-torsion point x=54130221868. 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 20:28:25",
  "updated_at": "2026-09-26 20:28:25"
}