{
  "id": 4680,
  "curve_key": "1663428121:-67842548013565",
  "ainvs": [
    "1",
    "0",
    "1",
    "-34654753",
    "78518579712"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 63.696439328973604,
  "faltings_height": 2.933465524256503,
  "conductor": "282151265615194",
  "bad_primes": [
    "2",
    "17",
    "19",
    "137",
    "263",
    "761",
    "937"
  ],
  "discriminant": "47936935725490230212",
  "regulator": "6097.528111644173670407888182209128252012766313577418",
  "points": [
    [
      "2761",
      "60958"
    ],
    [
      "3388",
      "-1020"
    ],
    [
      "4053",
      "66126"
    ],
    [
      "3441",
      "2478"
    ],
    [
      "-1327",
      "350190"
    ],
    [
      "40657/9",
      "-3274070/27"
    ],
    [
      "-6587",
      "-141620"
    ]
  ],
  "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 20:31:58",
  "updated_at": "2026-10-20 20:31:58"
}