{
  "id": 3486,
  "curve_key": "17164092864822023140799087722627446961:-67833610145852607257070185765302943240566381036921800041",
  "ainvs": [
    "1",
    "1",
    "1",
    "-357585268017125482099980994221405145",
    "78511122853996073065207742221224270468256045274555495"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 257.2076487760261,
  "faltings_height": 19.36947400690175,
  "conductor": "2774700096374548868697941163846920764265826133256711902170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "43",
    "211",
    "349",
    "1279",
    "1321",
    "1381",
    "2549",
    "15767",
    "58601",
    "407521",
    "1204681",
    "19629975401"
  ],
  "discriminant": "263453424019130340891552883112242274107583617046777894695027135298746204659847041181989518174296473600000000",
  "regulator": "166557639182156565147.7502449678432038175870283208048445044622454362580",
  "points": [
    [
      "436367904425598959",
      "74593788848706085046383080"
    ],
    [
      "-138559834988342037237487777/226472401",
      "890520691993236561938976947107962716712/3408183162649"
    ],
    [
      "-32334673496301996584137337/182007081",
      "906962413065040224076410674757764803448/2455457529771"
    ],
    [
      "-71981611334895918470177/3243601",
      "1717464128053591113598017046874331688/5841725401"
    ],
    [
      "-71742921369976977754513/113569",
      "8753577523888195469611813308727464/38272753"
    ],
    [
      "3000422110363073411257/10609",
      "1088947129672333688465647139026/1092727"
    ],
    [
      "9493418701686607673623/22201",
      "203731275184211567680442776639112/3307949"
    ],
    [
      "89450547725477665096623/201601",
      "7681756970030738599315102117291112/90518849"
    ],
    [
      "621918845310719667960887/1530169",
      "33601003606374885225370427383185864/1892819053"
    ],
    [
      "1616691537061762363015367/5929",
      "2055605182067286803658142200839524104/456533"
    ],
    [
      "471405565182214779354164047/2229445089",
      "11700799584440316886671469513538966528744/105267708767313"
    ],
    [
      "896492895387936362606983167/58874929",
      "26821926418671806397901752778116669705896/451747330217"
    ],
    [
      "2666692768900812844258389103/4839845761",
      "74348675494265537742377243891715430372392/336703229747009"
    ],
    [
      "6005247140560563430771247055/33497418529",
      "870635001210684441752615177489759996031128/6130798031433167"
    ],
    [
      "39889718302054752323142029167/97764404929",
      "707915935470821487790561470024285790945896/30568289782365217"
    ],
    [
      "462166352624941524318849543783/27656022601",
      "313995135278429243675591648771758741244244488/4599224214568901"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=11/5, t=383/1163. Found by sweeping t=a/b with the lossless conic-Hilbert prefilter of Breddin (Zenodo 10.5281/zenodo.22242109), screened with PARI ellrank (2-descent): 16 independent points, 2-Selmer upper bound 16.",
  "created_at": "2026-09-27 09:46:13",
  "updated_at": "2026-09-27 09:46:13"
}