{
  "id": 1929,
  "curve_key": "1514620205713740103858870777921:-26743676874768922225572300139638406751772701281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-31554587619036252163726474540",
    "30953329716167731427826379130819734911419600"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 213.8052545032379,
  "faltings_height": 15.874945019806342,
  "conductor": "96220149085890919907173196968787799179447574703830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "53",
    "83",
    "113",
    "127",
    "661",
    "857",
    "1459",
    "1697",
    "1811",
    "3049",
    "103903",
    "13470593",
    "39386881"
  ],
  "discriminant": "-411892130434918539681126771736175915091086745573083244150886380383131028680565112172680000",
  "regulator": "59517402113265.31811432613353910425135530546795766831119894707079",
  "points": [
    [
      "162264700075145369789247938903480/54406500635544121",
      "2064517176696842748728154582978000198946815593060/12690425684713444302477331"
    ],
    [
      "-241280978994370",
      "4951799266737307589360"
    ],
    [
      "642590686603460",
      "-16613759229510019902220"
    ],
    [
      "240442402875566300/361",
      "-119866851450237665635707940/6859"
    ],
    [
      "694510495734335/4",
      "44332456617034088837425/8"
    ],
    [
      "3368492710896614359720340/20321357809",
      "15939998354559322342912839636776731960/2896870519746377"
    ],
    [
      "-2397919116914195/16",
      "363822893468879632488715/64"
    ],
    [
      "2593796877483230",
      "-131907573898463468970190"
    ],
    [
      "466959242838585741145589590/9887370847561",
      "-169057817463111945080796733386773325296560/31090036753116912059"
    ],
    [
      "-2711157165151688369653/7873636",
      "-22010587436001327888469000236823/22093422616"
    ],
    [
      "424609280931023750",
      "-276684089600738209314042640"
    ],
    [
      "-2506559383701371596471213890760/11470602566608201",
      "-6432295913963036087464432030933945677907049660/1228511846955445707872699"
    ],
    [
      "-316241269983304",
      "3050469730823500168172"
    ]
  ],
  "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) = (3,2,135/4).",
  "created_at": "2026-09-25 19:16:58",
  "updated_at": "2026-09-25 19:16:58"
}