{
  "id": 616,
  "curve_key": "175421601002305930856410770718537223134326202801599632861691856:-2348693499993237568527101555596522666670625708820724201443236249079450400586117179402485837504",
  "ainvs": [
    "0",
    "1",
    "0",
    "-3654616687548040226175224389969525481965129225033325684618580",
    "2718395254621802741350811985642905251232189668096742750947829890903523661307068960191337600"
  ],
  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 429.988545729102,
  "faltings_height": 33.70061432638825,
  "conductor": "13256124609558049820392283796815008531233788836453627781721026792428981264573670000606421009825381988586278050067799482547057785910031781478625480",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "31",
    "47",
    "101",
    "139",
    "223",
    "281",
    "396572909",
    "1954266661",
    "210214586945260699",
    "1943268833199420515531429803",
    "70508602410815421111409529277204421106176714702669924666954151"
  ],
  "discriminant": "-68378572047130417487334760056959483812201379955471860174454228220382973263989782625036108150324260545734183213796040881004450495953118417417334995345846279288550615972682669436000000",
  "regulator": "48251869702606231173181657600401259.42580381629757590568774359959261688595158366917804250518152",
  "points": [
    [
      "935897991766755716616572751140",
      "-343226767999042843473278614700281241939172000"
    ],
    [
      "-10470781680719506117491219794270/9",
      "62716221212848834888037296242195326053501681090/27"
    ],
    [
      "227036695019678836042148215682370/169",
      "1061109242806649572268644874026184638712136957630/2197"
    ],
    [
      "1693499388266893954052853428640",
      "1177352567008053816459711895476056550148728000"
    ],
    [
      "44788751794809035458872773945610/49",
      "129053293116339595815402102479739258522971471250/343"
    ],
    [
      "-409054752915897992836410552030",
      "-2035899842993988200552255631357856279344091830"
    ],
    [
      "1072859873146108501143872717670",
      "-179988173760681297543422710275303882754932030"
    ],
    [
      "1105246015523238671396608840590",
      "171110260966812044361200686919826533435728950"
    ],
    [
      "278814799685867769772535102471940/361",
      "4095323396353410539199400771685001578813205956400/6859"
    ],
    [
      "14861546287229777235333831466770",
      "-56840204559518450685590196955281190098004704870"
    ],
    [
      "2768685041619853830949143191265/16",
      "92549657521862092085775022552719346724754488775/64"
    ],
    [
      "1121794642435438291537384225410",
      "174236219712568840570385836127547260563207830"
    ],
    [
      "1204661261768358540492807957540",
      "-253051526644856194765529656638438198512150400"
    ],
    [
      "2287582051854822144588470941590",
      "2515779994218103699716618494523656055454360050"
    ],
    [
      "-390674221777830302013432154380",
      "-2021517401698397538069458653012480907915324520"
    ],
    [
      "420592874262989803666711611930255/289",
      "-3411310148686205542707143052332536978536284848110/4913"
    ],
    [
      "2838667066790334810962461936758",
      "3901053913862016233995994956548294955219113006"
    ],
    [
      "-196536108504281571490441305285",
      "-1851774258888449870263133303772873313232278800"
    ],
    [
      "-2209998265223107554488720430960",
      "-35443089734105609449012387449166043869410600"
    ],
    [
      "411969863916931176859928494058424231165/74407876",
      "7918541489490173030849343591239824113792687974154395873475/641842338376"
    ],
    [
      "11795467096296840343497073349430",
      "40009370491304845166861936056002513769455653010"
    ],
    [
      "477627668669764432403263394580910/729",
      "15312335447169656844831125927176684244480406529550/19683"
    ],
    [
      "3569917309618927920091683893550",
      "-5930248503481104576054185122924793351587799190"
    ],
    [
      "99374454679002674419716151839423244790/71048041",
      "350748359423948267823514611479716455860625045467670352950/598863937589"
    ],
    [
      "-705165099347678730549372758130",
      "-2223702888429505366205239879398996471229046730"
    ],
    [
      "2956125090055987585737025653610022537430/3216818089",
      "67283508445426917430221486779940033466977025267038760515990/182448271553813"
    ],
    [
      "45726076529293586943265142462438772270/48288601",
      "109669229709847412197154878584176747346607527140046704370/335557488349"
    ],
    [
      "29069419154493941014846400607074/25",
      "-25317973010317369512255934503736873663370142318/125"
    ]
  ],
  "submitter": "Mundoamundo",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-11 19:24:48"
    }
  ],
  "commentary": "Fiber t = -2057/22382 of a rank-17 elliptic fibration of Elkies' K3 surface (arXiv:2608.25406). Found by a Mestre-Nagao sieve over t = a/b re-scored at 2^20, then an iterated 2-covering point search (fake 2-descent over 3000 cosets of the growing known lattice at level 0, minimal reduced quartic models, ratpoints). Basis LLL-reduced with respect to the canonical height. The 28 points are certified independent by the F2-rank of their images under the 2-descent map at the good primes.",
  "created_at": "2026-09-06 22:22:56",
  "updated_at": "2026-09-11 19:24:48"
}