{
  "id": 5045,
  "curve_key": "1694016176336588208:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-35292003673678921",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 125.92090145781673,
  "faltings_height": 8.561648866459551,
  "conductor": "1129344117557725472",
  "bad_primes": [
    "2",
    "13",
    "137",
    "313",
    "337"
  ],
  "discriminant": "2813253846020425771713195150433606693631780763133504",
  "regulator": "654823.959589476301079344791517812065371312452653",
  "points": [
    [
      "-3873789412/169",
      "1961262738655362/2197"
    ],
    [
      "-294892637/9",
      "28589353943228/27"
    ],
    [
      "57925616229/289",
      "4859977078008780/4913"
    ],
    [
      "6353368906921/20736",
      "12650841181098263915/2985984"
    ],
    [
      "226180812164086637/151609969",
      "106711874405393842974119016/1866773548297"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 187861661. 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 01:49:39",
  "updated_at": "2026-10-21 01:49:39"
}