{
  "id": 452,
  "curve_key": "2640009912170024196769824336235037425:-4576329057871921724004950897310926481244460162586798025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-55000206503542170766038007004896613",
    "5296677150314724213014972255851724752418661641474817"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 251.72098436534117,
  "faltings_height": 18.926451368227795,
  "conductor": "2370458085180475003482735023025170108836693446674620297777501668599438211647550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "67",
    "48699141226693",
    "313741437670571",
    "35290476238827690372768417782626907968141"
  ],
  "discriminant": "-1471548838868147549133553708559492561674695419611207333816195379402867092381604973017484205937413201920000",
  "regulator": "160280604755817816591.185079863063327786954357799276134982025293230315618192913",
  "points": [
    [
      "163755056272540722",
      "26102197601152179420807399"
    ],
    [
      "-197572972942892558",
      "-91929074348041884862094681"
    ],
    [
      "176498478865401682",
      "-32976572546372706447703001"
    ],
    [
      "2139194728885146922",
      "-3110775664649129924047307201"
    ],
    [
      "324756012103404442",
      "147261328040051441332421239"
    ],
    [
      "295670061256904862",
      "121993735826229706786585359"
    ],
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      "223672653539085922",
      "64690464270159869489758279"
    ],
    [
      "118987737166170862",
      "20903710771345285947917359"
    ],
    [
      "-267215363843855438",
      "-30221150767928227239959321"
    ],
    [
      "503798331385531567/4",
      "153341402070661451648313785/8"
    ],
    [
      "117378210822725842",
      "-21402022445571714147667961"
    ],
    [
      "445474418786112562",
      "263056567923495052498536679"
    ],
    [
      "97732045716674722",
      "29238454850225985847285399"
    ],
    [
      "95076809147933602",
      "-30444856805500685223942761"
    ],
    [
      "264380813210707378",
      "-96099741082873399692211865"
    ],
    [
      "-200046647835341318",
      "91069671482131012252395319"
    ],
    [
      "591674301971852242",
      "-424130768361456984296825081"
    ],
    [
      "141827552473968363442/961",
      "591373498823731363564773250489/29791"
    ],
    [
      "659550891840133282",
      "-505895984330369793635461481"
    ],
    [
      "-155587825844828172686/21025",
      "-230232370401279827009574053217353/3048625"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -13/19. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 20.",
  "created_at": "2026-08-30 15:55:04",
  "updated_at": "2026-08-30 15:55:04"
}