{
  "id": 4683,
  "curve_key": "339642016:-6259388370560",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-7075875",
    "7247021091"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 58.93020818032332,
  "faltings_height": 2.463176781869173,
  "conductor": "2769734719104",
  "bad_primes": [
    "2",
    "3",
    "17",
    "41",
    "43",
    "59",
    "4079"
  ],
  "discriminant": "22595495838450432",
  "regulator": "4631.2810045770810261403770065849199462601431736267",
  "points": [
    [
      "-2542",
      "93817"
    ],
    [
      "9695",
      "921854"
    ],
    [
      "21991/9",
      "1819234/27"
    ],
    [
      "1519",
      "1158"
    ],
    [
      "132655/81",
      "5082434/729"
    ],
    [
      "20513/16",
      "1072777/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the six supplied rational points exactly on this minimal model. The source records rank 6 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:37:10",
  "updated_at": "2026-10-20 20:37:10"
}