{
  "id": 5922,
  "curve_key": "4995885591812473302235319373376:-11166535939079355676242089034685326555115994624",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-104080949829426527129902486945",
    "12924231410971511170781990636024467554435457"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 212.05850244559505,
  "faltings_height": 15.228051781230475,
  "conductor": "9875976805007283687791280130029120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "29",
    "47",
    "53",
    "71",
    "89",
    "157",
    "179",
    "199",
    "263",
    "1051",
    "2243",
    "20123"
  ],
  "discriminant": "85858133953940316909267825732161036619616178264636016076527157625541383769600000000",
  "regulator": "74714431359.81044174169388408931472394099386986875114657551",
  "points": [
    [
      "-291861078835781",
      "4294163449795184821500"
    ],
    [
      "193789843468219",
      "179113866041094037500"
    ],
    [
      "-21021325338192923379/61009",
      "42299675403369824973690789800/15069223"
    ],
    [
      "-11315889467001459/289",
      "20220755178704163381691000/4913"
    ],
    [
      "116223016106007021/625",
      "104150466057725523657944/15625"
    ],
    [
      "993349360665811051/5329",
      "738540283195991847106500/389017"
    ],
    [
      "675249240843204421513/30976",
      "17544817779551144686249911870555/5451776"
    ],
    [
      "2219552936723454344619/11895601",
      "292711467502703422040865687500/41027927849"
    ],
    [
      "3797946706972784497941/20403289",
      "35910772488699955930274208200/92161656413"
    ],
    [
      "8916753531406619",
      "-841452613403016613958100"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein's elliptic-curves-by-rank collection, families/family_Z4.add_2026-10-24.part2.tsv.gz, 208336th data row, added on 24 October 2026:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/families/family_Z4.add_2026-10-24.part2.tsv.gz\r\n\r\nThe source lists proven rank 10 and torsion Z/4. I checked all ten supplied points exactly on this minimal model and independently verified their independence. I checked the supplied torsion generator has exact order 4 and computed the full torsion group separately. Conductor 9875976805007283687791280130029120. The source does not identify the construction method.",
  "created_at": "2026-10-25 21:42:32",
  "updated_at": "2026-10-25 21:42:32"
}