{
  "id": 5674,
  "curve_key": "-665424873744:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "13863018203",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 81.67107474441968,
  "faltings_height": 4.874163307009797,
  "conductor": "6149864758294699174688",
  "bad_primes": [
    "2",
    "17",
    "19",
    "157",
    "461",
    "593"
  ],
  "discriminant": "-170511374180455219794217641691328",
  "regulator": "2505937.87000809512904128761930166145265784233670748720",
  "points": [
    [
      "78831",
      "39783378"
    ],
    [
      "24021",
      "18624282"
    ],
    [
      "2264893/9",
      "-3763186334/27"
    ],
    [
      "16284825/4",
      "65744009835/8"
    ],
    [
      "5500652/121",
      "35817495498/1331"
    ],
    [
      "30071623/441",
      "329043698866/9261"
    ],
    [
      "405612",
      "-268988358"
    ],
    [
      "1768919/121",
      "-19093711686/1331"
    ]
  ],
  "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": "2026-10-24 04:21:24",
  "updated_at": "2026-10-24 04:21:24"
}