{
  "id": 5705,
  "curve_key": "-27843871872:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "580080664",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 72.14963621581364,
  "faltings_height": 4.080710096292627,
  "conductor": "1345974306986723584",
  "bad_primes": [
    "2",
    "17",
    "43",
    "281",
    "353"
  ],
  "discriminant": "-12492378715580775292658876416",
  "regulator": "21445971.51718009398309453496004516316720651221274281",
  "points": [
    [
      "81",
      "216765"
    ],
    [
      "5625",
      "1854975"
    ],
    [
      "148225/9",
      "101099845/27"
    ],
    [
      "212521/9",
      "139943465/27"
    ],
    [
      "3294225/169",
      "9504016995/2197"
    ],
    [
      "3697929/784",
      "37000875675/21952"
    ],
    [
      "60980481/2401",
      "656265900165/117649"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5671:\r\nhttps://elliptic-rank.icarm.cloud/curve/5671\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 - 145020166*x.\r\n\r\nWriting A = -145020166, 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 + 580080664*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 1345974306986723584, equal to the source conductor.",
  "created_at": "2026-10-24 14:07:20",
  "updated_at": "2026-10-24 14:07:20"
}