{
  "id": 4982,
  "curve_key": "513587344926267518750214976:-11639153511439003558596371480063529012224",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-10699736352630573307296145",
    "13471242490095005882715195700435220257"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 184.51038703196463,
  "faltings_height": 12.903789358825282,
  "conductor": "13704597129031349112713850720",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "37",
    "53",
    "113",
    "191",
    "919",
    "82613",
    "168037"
  ],
  "discriminant": "26959236470374372008904438065664345751147587902470889170716159311360000",
  "regulator": "240312722.85320994371861341084986817856595564278672184670",
  "points": [
    [
      "1830055310329",
      "138476936410184460"
    ],
    [
      "1904486668049",
      "37982920364371380"
    ],
    [
      "2096925359944",
      "505050519285358725"
    ],
    [
      "556512477728241/289",
      "435325336189557951500/4913"
    ],
    [
      "1003912470195177/529",
      "266485053032139033620/12167"
    ],
    [
      "22070954879432441/1849",
      "3166883999423139884900220/79507"
    ],
    [
      "55447505814068017/29241",
      "91220830235782993172636/5000211"
    ],
    [
      "118321094867098513/63001",
      "392458503525282963049380/15813251"
    ],
    [
      "444473311327065816/235225",
      "218561766470974663490039/114084125"
    ]
  ],
  "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 01:07:48",
  "updated_at": "2026-10-21 01:07:48"
}