{
  "id": 4678,
  "curve_key": "2214111865:-104183242418125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-46127331",
    "120578612558"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 64.55435158846014,
  "faltings_height": 2.979031178212734,
  "conductor": "153306369327950",
  "bad_primes": [
    "2",
    "5",
    "29",
    "109",
    "239",
    "349",
    "401"
  ],
  "discriminant": "42502657832480858000",
  "regulator": "7032.840127861517786234198663890684597249988619740674",
  "points": [
    [
      "-853",
      "399556"
    ],
    [
      "3931",
      "-1104"
    ],
    [
      "103",
      "340284"
    ],
    [
      "4971",
      "116356"
    ],
    [
      "4883",
      "106064"
    ],
    [
      "302",
      "326461"
    ],
    [
      "6247",
      "272956"
    ]
  ],
  "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 20:28:31",
  "updated_at": "2026-10-20 20:28:31"
}