{
  "id": 1932,
  "curve_key": "8638742380856619124558103510241:23499939190710704695850423407788276360475317039",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-179973799601179565094960489797",
    "-27199003692952159515636237908567379454872131"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 213.70142941281466,
  "faltings_height": 15.767547163979009,
  "conductor": "2848415887139195817481684276358617283728873972605630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "61",
    "167",
    "173",
    "193",
    "197",
    "211",
    "349",
    "601",
    "709",
    "2213",
    "52201",
    "175621",
    "1134769",
    "34412689"
  ],
  "discriminant": "53497569865809061764003661357827292194298253688166674793844878590920812182617673434400000",
  "regulator": "340960512803904.6349739256383882859366766244155573364650731650186",
  "points": [
    [
      "-190300819759463",
      "-398155048562486108524"
    ],
    [
      "-226990250192873",
      "1399184960247620966336"
    ],
    [
      "9137875172505277/16",
      "-480208753604198367677551/64"
    ],
    [
      "-297324884850223",
      "165967515262524246836"
    ],
    [
      "13608222212280697",
      "-1586677282597752428834284"
    ],
    [
      "392574763133307589/16",
      "-245933811538906905460117057/64"
    ],
    [
      "365678253760023964123223/726140809",
      "-61506999404501044042179973499931632/19567316380123"
    ],
    [
      "1176395092169627",
      "-37270635644190839533664"
    ],
    [
      "-158371674407822951213/707281",
      "-814111030453610794235910732544/594823321"
    ],
    [
      "529729090626517",
      "-5110035534009175739404"
    ],
    [
      "-77388991405479960579229488896596027/289238316077989653904",
      "6600662588447024372781423118082099129523856822587833/4919078312637627888320090454208"
    ],
    [
      "336570969930623107",
      "-195260607725371999779087364"
    ],
    [
      "1991618953481724127",
      "-2810666816229827256027603664"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 13, torsion Z/2Z: 13 independent points; 2-isogeny Selmer bound 13, confirmed by a second 2-isogeny descent. Specialisation of Kihara's rank-8 family (S. Kihara, Proc. Japan Acad. 77A (2001) 11-12) with u = (s^2 - l)/(2s), (p,q,s) = (1,-11,45/2).",
  "created_at": "2026-09-25 19:17:33",
  "updated_at": "2026-09-25 19:17:33"
}