{
  "id": 602,
  "curve_key": "1751044953236099686186887522588144465952441:-2274356968429967860003256304277685932438783771181645034376658989",
  "ainvs": [
    "1",
    "0",
    "1",
    "-36480103192418743462226823387253009707343",
    "2632357602349499837963691825055360859848962314696484742682558"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 291.80635989485205,
  "faltings_height": 22.209629863014495,
  "conductor": "1322983321576836290387546565476702569430136772677001665842838027055986763561121788830063975968070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "47",
    "97",
    "109",
    "103645879",
    "21275384581265073964905283",
    "185273691476118527364621845918259349307341983387971"
  ],
  "discriminant": "113588901487193032681354200011395746133901153664116397262105544379734963625336365737391866981966740638730770277901117312500",
  "regulator": "9897757794489524625159216.94562781584850037223360806022020093320780950568687480752830",
  "points": [
    [
      "88844935091396830099",
      "304262733441812919496062232730"
    ],
    [
      "15065383434148547539",
      "-1444364976912842012256234976990"
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      "198788395516553472019",
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      "-111149503024387660976",
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      "-412535233809408278556111229510"
    ],
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      "366892479570814059991/4",
      "1926112295394128740998128733985/8"
    ],
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    ],
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      "144253015716457077469",
      "-609708107616874818065266893160"
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      "851707294137214308469",
      "-24277458382992449173650642093310"
    ],
    [
      "1190449089956221971031/4",
      "-34068976873928521100103905512295/8"
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      "72454240541552024194",
      "-607927990458186476112878058235"
    ],
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      "219878209023295808752",
      "-2289433027214946106910757345115"
    ],
    [
      "15126708487933083769234/361",
      "-7442351411109203175818070932434840/6859"
    ],
    [
      "-211651758904023292088",
      "-933908220655844993989506455035"
    ],
    [
      "1117089680901939271306/9",
      "-3481051580646410112817852689280/27"
    ],
    [
      "186187140040625954269",
      "1514770596266249072814125572490"
    ],
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      "148971038656097167549",
      "-709858578952343091946882106920"
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      "252185893586879573098429644322310"
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      "-12610695743489322817930883981710"
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  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -425/132. 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 15:45:45",
  "updated_at": "2026-09-06 15:45:45"
}