{
  "id": 4976,
  "curve_key": "412626443655449616400:-8159343197944933524372013448000",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-8596384242821867008",
    "9443684259746171511926749012"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 142.4072230883119,
  "faltings_height": 9.776479286475315,
  "conductor": "93586594633890747391200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "29",
    "59",
    "61",
    "67",
    "269",
    "271",
    "15913"
  ],
  "discriminant": "2129130222836604113794529652503469882115799555299080000000",
  "regulator": "8502665.49170573374779407523905929068724175501528670962",
  "points": [
    [
      "-1045102028",
      "131477307757950"
    ],
    [
      "3027473036",
      "105673782772578"
    ],
    [
      "-26430075797163/8281",
      "49804821041493580700/753571"
    ],
    [
      "-661152906683/196",
      "20966239521992325/2744"
    ],
    [
      "-4457095307/9",
      "3146332742482600/27"
    ],
    [
      "64996495677/49",
      "6640648797656672/343"
    ],
    [
      "1008440591908/289",
      "727629655251115650/4913"
    ],
    [
      "53216740563037/36481",
      "19526360875383387300/6967871"
    ]
  ],
  "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. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 00:52:04",
  "updated_at": "2026-10-21 00:52:04"
}