{
  "id": 6305,
  "curve_key": "7847540761200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-163490432525",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 89.07366395943833,
  "faltings_height": 5.491045741594685,
  "conductor": "34213275554830819680800",
  "bad_primes": [
    "2",
    "5",
    "7",
    "23",
    "41",
    "61",
    "109",
    "149"
  ],
  "discriminant": "279677160927815003140713721901000000",
  "regulator": "54804008.9933258283500453743725803037305911834649669102",
  "points": [
    [
      "-1525",
      "15789850"
    ],
    [
      "-26158469204/793881",
      "51744107170136206/707347971"
    ],
    [
      "-30956436/625",
      "1395463803762/15625"
    ],
    [
      "-5452180/121",
      "113528018050/1331"
    ],
    [
      "-33005/9",
      "661090150/27"
    ],
    [
      "11937025/9",
      "39279238550/27"
    ],
    [
      "170380625/169",
      "2037275209250/2197"
    ],
    [
      "1311349025/1024",
      "45058139834575/32768"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8. Rank proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file families/family_Z2.add_2026-10-24.part1.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:56:18",
  "updated_at": "2026-10-31 23:56:18"
}