{
  "id": 6332,
  "curve_key": "-9400464:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "195843",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 48.168808823172334,
  "faltings_height": 2.0823078135725184,
  "conductor": "1227343380768",
  "bad_primes": [
    "2",
    "3",
    "97",
    "673"
  ],
  "discriminant": "-480733219439494848",
  "regulator": "1649.77359664740444792390701484271963684889826156",
  "points": [
    [
      "48",
      "3084"
    ],
    [
      "97",
      "4462"
    ],
    [
      "108",
      "4734"
    ],
    [
      "867",
      "28662"
    ],
    [
      "1164",
      "42486"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "OEIS A309028, a(5)=195843, contributed by Vaclav Kotesovec (14 July 2019); sequence by Seiichi Manyama. Curve y²=x³+195843x.\r\n\r\nPARI/GP 2.17.4 returned rank bounds [5,5]. All five displayed points pass exact substitution. Exact 2-descent quadratic characters at 12 good primes give matrix rank 6 with torsion-row rank 1, certifying five independent points modulo torsion. Torsion Z/2Z; conductor 1227343380768.\r\n\r\nSource: https://oeis.org/A309028",
  "created_at": "2026-11-01 01:57:35",
  "updated_at": "2026-11-01 01:57:35"
}