{
  "id": 601,
  "curve_key": "207686622503017847739624155286030425787201:-98777041416902720368790280317873853092060073913976224108660449",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-4326804635479538494575503235125633870567",
    "114325279417711481909403784860112770146861553949957593778591"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 285.49594156614125,
  "faltings_height": 21.72153228012139,
  "conductor": "530500502593057961420036692544358590035411455325690626851040620565705409063433583480522570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "41",
    "71",
    "101",
    "39119573617",
    "5483272733966728699",
    "41296297010177354778585591507548109010253977861"
  ],
  "discriminant": "-462155413041608288091056862837014184008286992858321568755049644026481538233970319862396301064751594597674435872000000000",
  "regulator": "476678640711692755093848.460724425337555568201413223228202959764222945229417176233270",
  "points": [
    [
      "40158774589305851971",
      "-73015440340778830330179983986"
    ],
    [
      "-74039817233057181469",
      "169713388732479893437279656494"
    ],
    [
      "69546330869914832971",
      "-387022072192695900987784724986"
    ],
    [
      "171087061558117220371",
      "-2093302935284804190684050517586"
    ],
    [
      "1868752084528448611",
      "-325954107746241634349535365266"
    ],
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      "-34483346064982554941",
      "-471724277877709464751167737074"
    ],
    [
      "32149138604578460671",
      "91926763498395889475392583714"
    ],
    [
      "32832394079764138351",
      "-87510755655075361816308060706"
    ],
    [
      "36265969014519723971",
      "-71465115888076082273633771986"
    ],
    [
      "29522136131294786471",
      "110990874551246846267766915514"
    ],
    [
      "293505988914939530221",
      "-4912095307492142091441094965736"
    ],
    [
      "-22787008418788892269",
      "448428489473346330736975986094"
    ],
    [
      "78724801810516915776379/1849",
      "-6786797255865748893736648700378902/79507"
    ],
    [
      "76944175596218063099/4",
      "-1563841425376743331786775160323/8"
    ],
    [
      "150209267139468452771",
      "1689243728306393231431376714414"
    ],
    [
      "30308906801398504771",
      "105010603834626209523013370414"
    ],
    [
      "114852513191812990631",
      "-1064148417893776715862025851206"
    ],
    [
      "466577463963585854371",
      "9983330977705618342469045546414"
    ],
    [
      "216270814446795873971",
      "3048641109947657742773421498014"
    ],
    [
      "38558790626936630971",
      "-69407326903013504879133899986"
    ],
    [
      "2075251557014565421",
      "-324584363121989869084376580136"
    ],
    [
      "-64904344906981900829",
      "348911657581124836219995333614"
    ],
    [
      "-60330172293948077029",
      "-394685481482170020747820454986"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -172/17. The 6 points beyond the seventeen generic sections come from the surface's rational quadratic sections: writing x_tau = a/c^2 and y_tau = b/c^3 for a trace of height 10, the slope of the bisection is forced to be kappa/c with kappa = -b*a^(-1) mod c^2 of degree 5, so each section's point on this fibre is obtained by one polynomial evaluation and one square test rather than by any search. Claimed lower bound: rank >= 23.",
  "created_at": "2026-09-06 15:45:33",
  "updated_at": "2026-09-06 15:45:33"
}