{
  "id": 4673,
  "curve_key": "12060716329:-1316242972181717",
  "ainvs": [
    "1",
    "1",
    "0",
    "-251264923",
    "1523324672233"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 69.63965827073807,
  "faltings_height": 3.6484339422196697,
  "conductor": "398805545629455510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "59",
    "197",
    "22129",
    "567961"
  ],
  "discriminant": "12654415019203670602152900",
  "regulator": "26282.6545868870839016702312308743689748848648320437807",
  "points": [
    [
      "11284",
      "347893"
    ],
    [
      "-18291",
      "22568"
    ],
    [
      "8377",
      "-84281"
    ],
    [
      "-14456",
      "1468363"
    ],
    [
      "10324",
      "167413"
    ],
    [
      "40411/4",
      "975569/8"
    ],
    [
      "4719",
      "663013"
    ],
    [
      "6784",
      "-365357"
    ]
  ],
  "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 eight supplied rational points exactly on this minimal model. The source records rank 8 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:22:37",
  "updated_at": "2026-10-20 20:22:37"
}