{
  "id": 5700,
  "curve_key": "6373897805376:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-132789537612",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 88.44969689625276,
  "faltings_height": 5.43904848632922,
  "conductor": "3918458066490836147232",
  "bad_primes": [
    "2",
    "3",
    "107",
    "241",
    "313",
    "457"
  ],
  "discriminant": "149855107622782948826743536102715392",
  "regulator": "328232178.936002472017700778234323189550409734056126313",
  "points": [
    [
      "3767481/4",
      "-6743202867/8"
    ],
    [
      "4932841/4",
      "10466611307/8"
    ],
    [
      "34550884/9",
      "-202173092884/27"
    ],
    [
      "35354916",
      "-210209163948"
    ],
    [
      "515524",
      "-261824444"
    ],
    [
      "132204004/289",
      "918918527284/4913"
    ],
    [
      "45927729/4",
      "-311095426761/8"
    ],
    [
      "188156089/196",
      "2387761768909/2744"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5672:\r\nhttps://elliptic-rank.icarm.cloud/curve/5672\r\n\r\nRubinstein reports rank 8 proved, with eight independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 + 33197384403*x.\r\n\r\nWriting A = 33197384403, the rational 2-isogeny\r\n(x,y) -> (x + A/x, y*(x^2-A)/x^2)\r\ngives the global minimal model y^2 = x^3 - 132789537612*x.\r\n\r\nThe eight submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 3918458066490836147232, equal to the source conductor.",
  "created_at": "2026-10-24 13:48:01",
  "updated_at": "2026-10-24 13:48:01"
}