{
  "id": 5042,
  "curve_key": "207509310198429888:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-4323110629133956",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 119.62185780600315,
  "faltings_height": 8.036728562141752,
  "conductor": "69169770066143296",
  "bad_primes": [
    "2",
    "11",
    "29",
    "257",
    "401"
  ],
  "discriminant": "5170934326187742978651838259482225840884363956224",
  "regulator": "101933.752901090032038746570907439878171150273527",
  "points": [
    [
      "-45344052",
      "320618490348"
    ],
    [
      "-36443198",
      "330374820336"
    ],
    [
      "3413280222",
      "199378041340896"
    ],
    [
      "5346849277/81",
      "34674734198951/729"
    ],
    [
      "71313900445150/986049",
      "250845325472752024960/979146657"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 65750366. 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 01:49:27",
  "updated_at": "2026-10-21 01:49:27"
}