{
  "id": 5542,
  "curve_key": "191530918955376:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3990227478237",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 98.65821110460767,
  "faltings_height": 6.28975800369213,
  "conductor": "467861607436623935607072",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "31",
    "61",
    "107",
    "199"
  ],
  "discriminant": "4066052099088521697431271526257450115392",
  "regulator": "55612473440.2326761116153488810685193522205726058920348",
  "points": [
    [
      "26735193081/4",
      "-4371444490251483/8"
    ],
    [
      "10398492729/841",
      "1046435970224826/24389"
    ],
    [
      "1215711323649/289",
      "-1340434644347007126/4913"
    ],
    [
      "32097947281/1156",
      "-5735735400831857/39304"
    ],
    [
      "1404292956366609/29116816",
      "-52579173867837950808441/157114339136"
    ],
    [
      "174046251490281/73599241",
      "-1228947052119631112178/631407888539"
    ],
    [
      "819171616561/268324",
      "-560678986774314143/138991832"
    ],
    [
      "6369000349404289/2528100",
      "508284390378237264670663/4019679000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of ICARM curve #5533: https://elliptic-rank.icarm.cloud/curve/5533. Michael Rubinstein submitted #5533 as proved rank 8, with eight independent listed points matching its 2-descent upper bound. Starting from y^2 = x^3 + Ax with A = 15960909912948, apply the standard rational 2-isogeny (x,y) ↦ (x + A/x, y(1 − A/x^2)) to y^2 = x^3 − 4Ax, then reduce by the rational fourth-power scaling (x,y) = (4X,8Y). This gives the submitted model y^2 = x^3 − 3990227478237x. The eight submitted points are the exact transported images and were checked on the submitted model. The rational isogeny preserves rank and conductor; the conductor is 467861607436623935607072.",
  "created_at": "2026-10-23 00:02:39",
  "updated_at": "2026-10-23 00:02:39"
}