{
  "id": 4985,
  "curve_key": "-34688539643394980852990975:-210685056680603330659466955604936282625",
  "ainvs": [
    "1",
    "1",
    "1",
    "722677909237395434437312",
    "243848445232480896651380113381173281"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 176.48685548764882,
  "faltings_height": 12.827470743709746,
  "conductor": "50215092951230658153897413550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "29",
    "47",
    "89",
    "139",
    "181",
    "349",
    "4889",
    "12541",
    "5126089"
  ],
  "discriminant": "-49843016132592967479488105712734385224565656602761390965928902274345000000",
  "regulator": "4386557568.5460470750075192678696473857115271622892061242",
  "points": [
    [
      "-27635000081",
      "473134388482574513"
    ],
    [
      "1211925789705",
      "1702853925936446197"
    ],
    [
      "-23258591894806719/259081",
      "55675651542668907042386165/131872229"
    ],
    [
      "889416355221/16",
      "34118230472953762567/64"
    ],
    [
      "17911177544125/16",
      "100292338224165522443/64"
    ],
    [
      "375885055107105/121",
      "7584044952699751429907/1331"
    ],
    [
      "78844341380762625/380689",
      "149000436305790945946748081/234885113"
    ],
    [
      "96059329560549900975/50027329",
      "1044340639042906295363468350079/353843298017"
    ],
    [
      "156951672596329499541/76860289",
      "2155713128414027189780939601619/673834153663"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, families/family_Z4.part2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Nine rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 01:11:20",
  "updated_at": "2026-10-21 01:11:20"
}