{
  "id": 4688,
  "curve_key": "1005232081:-31849421399225",
  "ainvs": [
    "1",
    "1",
    "1",
    "-20942335",
    "36854030276"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 62.18545283449866,
  "faltings_height": 2.9419598130081184,
  "conductor": "906500091605901",
  "bad_primes": [
    "3",
    "13",
    "43",
    "61",
    "97",
    "109",
    "113",
    "7417"
  ],
  "discriminant": "806057161955692351497",
  "regulator": "9076.390330985304963833611985018380107365545230585647",
  "points": [
    [
      "-2274",
      "270811"
    ],
    [
      "3037",
      "34189"
    ],
    [
      "2402",
      "19203"
    ],
    [
      "9478",
      "825867"
    ],
    [
      "-4237/4",
      "1928397/8"
    ],
    [
      "49229/16",
      "2427459/64"
    ],
    [
      "-4308",
      "219283"
    ]
  ],
  "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 20:40:36",
  "updated_at": "2026-10-20 20:40:36"
}