{
  "id": 4943,
  "curve_key": "0:729000",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-844"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 26.99885802198159,
  "faltings_height": 0.30756074429009456,
  "conductor": "675",
  "bad_primes": [
    "3",
    "5"
  ],
  "discriminant": "-307546875",
  "regulator": "1.216773260922917078654279593465475939824",
  "points": [
    [
      "10",
      "-13"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4873, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4873.\r\n\r\nThe source model is y^2 + y = x^3 + 31. Its public entry supplies one rational point and no commentary identifying an earlier source.\r\n\r\nCompleted the square with Y = y + 1/2, giving Y^2 = x^3 + B with B = 125/4. Applied the standard degree-3 isogeny X = (x^3+4*B)/x^2, V = Y*(x^3-8*B)/x^3, then set y' = V - 1/2. The resulting integral model is y'^2 + y' = X^3 - 844.\r\n\r\nOne supplied rational point transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 675. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:27:05",
  "updated_at": "2026-10-20 23:27:05"
}