{
  "id": 4692,
  "curve_key": "12679089241:-1427683664960605",
  "ainvs": [
    "1",
    "0",
    "1",
    "-264147693",
    "1652389636952"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 69.78965987086887,
  "faltings_height": 3.3497131145614847,
  "conductor": "1294885748254202",
  "bad_primes": [
    "2",
    "13",
    "17",
    "53",
    "61",
    "113",
    "157",
    "3929"
  ],
  "discriminant": "529111034908639004432",
  "regulator": "22388.22306212235468213469021951528243802948797696061",
  "points": [
    [
      "9335",
      "3418"
    ],
    [
      "9270",
      "14338"
    ],
    [
      "9391",
      "-3570"
    ],
    [
      "9371",
      "-2702"
    ],
    [
      "9374",
      "-6137"
    ],
    [
      "9400",
      "-1977"
    ],
    [
      "9378",
      "-4025"
    ]
  ],
  "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 20:45:07",
  "updated_at": "2026-10-20 20:45:07"
}