{
  "id": 5704,
  "curve_key": "-36209060544:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "754355428",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 72.93772564719366,
  "faltings_height": 4.146384215574296,
  "conductor": "1138104223506126368",
  "bad_primes": [
    "2",
    "73",
    "109",
    "137",
    "173"
  ],
  "discriminant": "-27473123156210291742551216128",
  "regulator": "15523016.47554599507536130658263644130604623566315343",
  "points": [
    [
      "2304",
      "1322976"
    ],
    [
      "1721344/9",
      "2281570624/27"
    ],
    [
      "1089936",
      "1138254408"
    ],
    [
      "1382976/169",
      "5695746672/2197"
    ],
    [
      "1008016/9",
      "1042033528/27"
    ],
    [
      "21455424/361",
      "109480293744/6859"
    ],
    [
      "44944/81",
      "471734344/729"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5670:\r\nhttps://elliptic-rank.icarm.cloud/curve/5670\r\n\r\nRubinstein reports rank 7 proved, with seven independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 - 188588857*x.\r\n\r\nWriting A = -188588857, 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 + 754355428*x.\r\n\r\nThe seven 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 1138104223506126368, equal to the source conductor.",
  "created_at": "2026-10-24 14:05:48",
  "updated_at": "2026-10-24 14:05:48"
}