{
  "id": 5701,
  "curve_key": "-5280234701184:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "110004889608",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 87.88497499092186,
  "faltings_height": 5.391988327551646,
  "conductor": "5378255883408118397184",
  "bad_primes": [
    "2",
    "3",
    "19",
    "41",
    "67",
    "73",
    "401"
  ],
  "discriminant": "-85195360042255667965423653801197568",
  "regulator": "251047694.952063390302321286476676693719148735105120825",
  "points": [
    [
      "474721",
      "399004723"
    ],
    [
      "994009",
      "1044739351"
    ],
    [
      "833569/4",
      "1430503921/8"
    ],
    [
      "213949129/484",
      "3912374860091/10648"
    ],
    [
      "173949721/3481",
      "15399124557047/205379"
    ],
    [
      "2765569/441",
      "243284505661/9261"
    ],
    [
      "24373969/289",
      "488284244299/4913"
    ],
    [
      "5812921/441",
      "352926681337/9261"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5673:\r\nhttps://elliptic-rank.icarm.cloud/curve/5673\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 - 27501222402*x.\r\n\r\nWriting A = -27501222402, 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 + 110004889608*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 5378255883408118397184, equal to the source conductor.",
  "created_at": "2026-10-24 13:49:43",
  "updated_at": "2026-10-24 13:49:43"
}