{
  "id": 5041,
  "curve_key": "165537981981187248:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3448707957941401",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 118.9439311853185,
  "faltings_height": 7.980234677084699,
  "conductor": "110358654654124832",
  "bad_primes": [
    "2",
    "17",
    "47",
    "67",
    "1097"
  ],
  "discriminant": "2625120427778747314905924919043896314324461068864",
  "regulator": "206653.288915877337875015182657322714044926674948",
  "points": [
    [
      "-43633683",
      "259626145164"
    ],
    [
      "123286499",
      "1203628477380"
    ],
    [
      "3253786876",
      "185572196586810"
    ],
    [
      "-45852513424/37249",
      "468305188775130300/7189057"
    ],
    [
      "-1427932944/25",
      "12895067445204/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 58725701. 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 01:49:24",
  "updated_at": "2026-10-21 01:49:24"
}