{
  "id": 599,
  "curve_key": "1819767909546990633773841128349031505041:-78357603558112980334209193049549801722355119410211894892089",
  "ainvs": [
    "1",
    "0",
    "0",
    "-37911831448895638203621690173938156355",
    "90691670784852986494767987482904300661683284395472624577"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 271.2172666216104,
  "faltings_height": 20.463318834830055,
  "conductor": "3120065552430437518084446980377456978556342298121691656956566322835163731063945882578030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "43",
    "31183",
    "133391",
    "245893367",
    "2187124087688004925459",
    "9076706842899395697742478234233539422417"
  ],
  "discriminant": "-65770874146009551411416078978771259752043406805865231058980612946969450984819909568084282222646179399040000000000",
  "regulator": "616915036962952511384274.429113275492312362264657863368570567913264444125356891741200",
  "points": [
    [
      "10400118073602942094",
      "28658444828521471144532909353"
    ],
    [
      "-6869885821589511506",
      "-5187975271997018792723968247"
    ],
    [
      "2894917750466992594",
      "2280578082790935510887889853"
    ],
    [
      "3183090652798756494",
      "1505376821122742029339527753"
    ],
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      "-925869364932599754190384247"
    ],
    [
      "3940466906798198494",
      "-1576732187336854975969738247"
    ],
    [
      "48264129288729776206/49",
      "-2527628659142914535901695764721/343"
    ],
    [
      "-5508845383664178146",
      "11504915396418176941803032233"
    ],
    [
      "2302571996016992494",
      "-3950292725917596552320176247"
    ],
    [
      "52768254457124576494",
      "380818536312754104426380047753"
    ],
    [
      "956163863257818992494",
      "29565791302532754884146551823753"
    ],
    [
      "115763893806754277494",
      "1243819167717227784291985333753"
    ],
    [
      "33745239511072989586/9",
      "-30240234045885699076966804609/27"
    ],
    [
      "-7089700103115237506",
      "-1766233543922015402968006247"
    ],
    [
      "5724430955224457494",
      "-7826398635778546778660146247"
    ],
    [
      "3817111376531750434",
      "-1262772906523555916972778227"
    ],
    [
      "7090807986404072494",
      "-13356228673284921200723296247"
    ],
    [
      "3938773618232029294",
      "-1572080613968612204173897847"
    ],
    [
      "1713103296272144494",
      "5547275983084318954010959753"
    ],
    [
      "2119983298938512494",
      "4455011121153293955347743753"
    ],
    [
      "1397617332139828924",
      "6358887622306797601937304043"
    ],
    [
      "-5679359777621907506",
      "11082334042150727167354423753"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 275/13. 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 15:45:09",
  "updated_at": "2026-09-06 15:45:09"
}