{
  "id": 4689,
  "curve_key": "2251842313:-106853893690085",
  "ainvs": [
    "1",
    "1",
    "0",
    "-46913381",
    "123653940825"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 64.60504357170582,
  "faltings_height": 3.0501804148194864,
  "conductor": "1065080179392582",
  "bad_primes": [
    "2",
    "3",
    "19",
    "23",
    "73",
    "181",
    "577",
    "53281"
  ],
  "discriminant": "505467881696490350724",
  "regulator": "6680.486654247187310127681572040305427208665843252137",
  "points": [
    [
      "4848",
      "98523"
    ],
    [
      "3793",
      "15389"
    ],
    [
      "4031",
      "6107"
    ],
    [
      "3100",
      "88035"
    ],
    [
      "7413",
      "424449"
    ],
    [
      "3407/4",
      "2319547/8"
    ],
    [
      "-5800",
      "-445075"
    ]
  ],
  "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 seven supplied rational points exactly on this minimal model. The source records rank 7 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:42:44",
  "updated_at": "2026-10-20 20:42:44"
}