{
  "id": 5533,
  "curve_key": "-766123675821504:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "15960909912948",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 102.81709418796734,
  "faltings_height": 6.636331593972103,
  "conductor": "467861607436623935607072",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "31",
    "61",
    "107",
    "199"
  ],
  "discriminant": "-260227334341665388635601377680476807385088",
  "regulator": "217236224.375908891060997456566673903719611611741765761",
  "points": [
    [
      "597",
      "97614873"
    ],
    [
      "49132902",
      "345533063148"
    ],
    [
      "274134/289",
      "604516458924/4913"
    ],
    [
      "41585229/289",
      "7450368042411/4913"
    ],
    [
      "417240912/5041",
      "411464288433528/357911"
    ],
    [
      "1162840182/529",
      "82257125965812/12167"
    ],
    [
      "2037676221/1369",
      "263466004539843/50653"
    ],
    [
      "251928299844/25",
      "126449020000826172/125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Rank 8, proved: 8 independent points listed, matching the 2-descent upper bound. Torsion Z/2. Member of the family y^2 = x^3 + a x.",
  "created_at": "2026-10-22 22:49:54",
  "updated_at": "2026-10-22 22:49:54"
}