{
  "id": 1920,
  "curve_key": "21292666383726598974320523825:-14234107074828855045645827000294221710515625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-443597216327637478631677580",
    "16474660966237211646579344641191673788047"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 198.72842979413613,
  "faltings_height": 14.61732666743864,
  "conductor": "224593554269612009864883936329730274909323150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "29",
    "37",
    "41",
    "47",
    "127",
    "139",
    "197",
    "3319",
    "3919",
    "4441",
    "499267",
    "1076903"
  ],
  "discriminant": "-111664459112571378368425429361656266837613120057253819262564250987250741691744000000",
  "regulator": "2517556277538.603939439427739493163716286055381805267011739483042",
  "points": [
    [
      "54444683125045",
      "-392057881853855455499"
    ],
    [
      "-3886448811156382549446778539843595056555653/393305365112235770069336810449",
      "34789414802529491923648404420378513666573021188436919098532403697/246657772989928265522829479493323371006879207"
    ],
    [
      "1081695808660313571143352008205/227037481599157009",
      "-13012798004505072472888708246722400719336974869/108179841582145972652331527"
    ],
    [
      "-31166595826611",
      "5118080424921360205"
    ],
    [
      "-3634375412433976989/1014049",
      "-137071623535355541924027104335/1021147343"
    ],
    [
      "4021603197052907703505280811421/69338951244347409",
      "-7871318539209645476600781749455276773936563645/18258533932637022078408327"
    ],
    [
      "-416382544131",
      "129070891247409650365"
    ],
    [
      "-19769439317701006185272498411619/986770691481602329",
      "-129004226468348076201902066475152716102776051265/980221813129172282899979267"
    ],
    [
      "-26940109601198017379/14615329",
      "7346171158940552617267379126475/55874402767"
    ],
    [
      "-28609996001747",
      "-75814113592448041179"
    ],
    [
      "443755582428374949/841",
      "-295388708300165539455149455/24389"
    ],
    [
      "4988240985733",
      "-119941702069434398379"
    ],
    [
      "387479410716229/16",
      "9036258303565469309485/64"
    ]
  ],
  "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) = (3,-2,29/1).",
  "created_at": "2026-09-25 19:10:53",
  "updated_at": "2026-09-25 19:10:53"
}