{
  "id": 5882,
  "curve_key": "31289679313:-4814761830273305",
  "ainvs": [
    "1",
    "1",
    "1",
    "-651868319",
    "5572369395461"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 72.49966243712768,
  "faltings_height": 4.028698595740213,
  "conductor": "16417453512642",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "233",
    "337",
    "569",
    "673"
  ],
  "discriminant": "4312524477436178311261122624",
  "regulator": "2746.4771621275880943660429687975217067619917334362",
  "points": [
    [
      "-9417",
      "3302590"
    ],
    [
      "-26193",
      "2175802"
    ],
    [
      "19941",
      "-719456"
    ],
    [
      "1367",
      "2163530"
    ],
    [
      "235701/25",
      "63719384/125"
    ],
    [
      "1140147/4",
      "-1213818475/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein’s elliptic-curves-by-rank repository, torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz, 47th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b:\r\nhttps://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz\r\n\r\nThe source row reports proven rank 6 with torsion Z/2 × Z/2 and supplies these six generators on the minimal model. I checked all six points exactly and independently verified their independence. The full torsion group and supplied torsion generators were checked separately. Conductor 16417453512642. The construction author and search method are not identified in the source row.",
  "created_at": "2026-10-25 19:29:31",
  "updated_at": "2026-10-25 19:29:31"
}