{
  "id": 4939,
  "curve_key": "-384:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "8",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 17.85192765776318,
  "faltings_height": -0.44409895021157786,
  "conductor": "256",
  "bad_primes": [
    "2"
  ],
  "discriminant": "-32768",
  "regulator": "1.217418063953962721794380839188170690716",
  "points": [
    [
      "1",
      "3"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #2899, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/2899.\r\n\r\nThe source identifies y^2 = x^3 - 2*x as Cremona 256b1, LMFDB 256.b1: https://www.lmfdb.org/EllipticCurve/Q/256/b/1.\r\n\r\nApplied the standard degree-2 isogeny with kernel generated by (0,0). The coordinate map is X = (x^2-2)/x, Y = y*(x^2+2)/x^2, giving y^2 = x^3 + 8*x. The supplied source point (2,2) maps to (1,3), checked exactly on the target curve.\r\n\r\nRational torsion C2. Same rank and conductor as the source; conductor 256. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:22:03",
  "updated_at": "2026-10-20 23:22:03"
}