{
  "id": 5047,
  "curve_key": "11025451634392267968:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-229696909049838916",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 131.5402141768723,
  "faltings_height": 9.029924926380849,
  "conductor": "3675150544797422656",
  "bad_primes": [
    "2",
    "7",
    "23",
    "151",
    "9857"
  ],
  "discriminant": "775613620775158995702487560609235182918025849558994944",
  "regulator": "368051.804231135245655208194504322963425713184780",
  "points": [
    [
      "-1492638467499294687698/3347842343521",
      "22741504951962982371371402574336/6125583962206152431"
    ],
    [
      "-184893561160336/395641",
      "571945303534098900840/248858189"
    ],
    [
      "-880665975/16",
      "226058090411685/64"
    ],
    [
      "2080608313/4",
      "36881715664563/8"
    ],
    [
      "209577491876025/306916",
      "2161160793022671900915/170031464"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 479267054. Found by a Mestre-Nagao sieve over n <= 3*10^9 (n = 5,6,7 mod 8), top candidates checked with ellrank.",
  "created_at": "2026-10-21 01:49:47",
  "updated_at": "2026-10-21 01:49:47"
}