{
  "id": 5694,
  "curve_key": "-11331508553027664:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "236073094854743",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 110.89909082360478,
  "faltings_height": 7.309831313608555,
  "conductor": "1783376195657487548808627073568",
  "bad_primes": [
    "2",
    "19",
    "157",
    "197",
    "313",
    "769",
    "1669"
  ],
  "discriminant": "-842014275598281539037192974161391420269466048",
  "regulator": "25455918228.90717815547251096741520614721668041735827843323",
  "points": [
    [
      "78591541",
      "709918476372"
    ],
    [
      "401723293/3249",
      "1000577026554616/185193"
    ],
    [
      "772878067/9",
      "21827741272532/27"
    ],
    [
      "926209881/784",
      "367683402456483/21952"
    ],
    [
      "3624942825/64",
      "226136396322165/512"
    ],
    [
      "8335888929/484",
      "1019913608450889/10648"
    ],
    [
      "23280454537/7056",
      "16918690885812827/592704"
    ],
    [
      "97343800499/265225",
      "1271790935852104932/136590875"
    ],
    [
      "712255398489/8464",
      "611046992803773219/778688"
    ],
    [
      "16911666217179/2968729",
      "200057852440887377496/5115120067"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Rank 10, proved: 10 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 13:20:26",
  "updated_at": "2026-10-24 13:20:26"
}