{
  "id": 4651,
  "curve_key": "3541682656:-187451494295680",
  "ainvs": [
    "0",
    "1",
    "0",
    "-73785055",
    "216933153009"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 65.96360333314165,
  "faltings_height": 3.4758777236435257,
  "conductor": "148797332771970176",
  "bad_primes": [
    "2",
    "7",
    "17",
    "41",
    "79",
    "103",
    "167",
    "271",
    "647"
  ],
  "discriminant": "5374473654865220558358272",
  "regulator": "134355.976748964336635454046476177865521971302039903510",
  "points": [
    [
      "-8103",
      "531834"
    ],
    [
      "178880",
      "-75570247"
    ],
    [
      "70184",
      "18459557"
    ],
    [
      "80813/4",
      "-21125197/8"
    ],
    [
      "136825",
      "50513878"
    ],
    [
      "2249",
      "249742"
    ],
    [
      "13525/4",
      "-625649/8"
    ],
    [
      "-8920",
      "406747"
    ]
  ],
  "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. Eight supplied rational points checked exactly on the displayed model. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 17:32:25",
  "updated_at": "2026-10-20 17:32:25"
}