{
  "id": 4595,
  "curve_key": "51603764831357821991982698027727250763200:-15720551826493507152009977371754723815973914748697419616649600",
  "ainvs": [
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    "1",
    "0",
    "-1075078433986621291499639542244317724233",
    "18195083132515633277430966183757612134284743704318351981563"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 281.8201489389884,
  "faltings_height": 21.502432254444305,
  "conductor": "9281497273884032385186528170081105432870619335479591431082212913885764058460952904515687647400",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "29",
    "31",
    "89",
    "163",
    "997",
    "1823",
    "26723",
    "12950204567",
    "61287157423",
    "7153966458663330275159024012743280414303612447491"
  ],
  "discriminant": "-63493969483302358805700173285996889352501504303141641686348715559079738970866645922786893378351597345140172081706720000",
  "regulator": "1571625325451070369898098652.27545509665952170683573215208810855244107723267952200531840668",
  "points": [
    [
      "7328300453146984363",
      "103489827102602256847570479330"
    ],
    [
      "-103180569927148316923/4",
      "1356774310261299525288370599735/8"
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    [
      "88895528754827607181/9",
      "-2495107619553239833554599679998/27"
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      "87343593932236349903",
      "768524371607193462564460954830"
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      "-31990565948222476147",
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    [
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      "-4123555877093681502825041041626"
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    [
      "68388801507707832203",
      "514322961555330363521577128670"
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      "-116690809640921578920614623218"
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      "36480146018456994323",
      "-165903229726263613056903494130"
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    [
      "8802054882837427960187/169",
      "-706755844483833015328102751743110/2197"
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      "57798434090440602413",
      "-386189190927185487665593803330"
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      "-27972998563509365347",
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    [
      "-124267711006996424873/9",
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      "23656939270662787823",
      "77470267335049958516122928370"
    ],
    [
      "-525578586137913860691517/28561",
      "860027642441747434249183457522365470/4826809"
    ],
    [
      "78477208631877988787",
      "-645864798209414673479926004658"
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    [
      "-1980324513066466997952487/55696",
      "1407709988280403352965584108852024645/13144256"
    ],
    [
      "41968100647429187841542/121",
      "8561014147238084588934992164076757/1331"
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    [
      "-5773703192267331549097/169",
      "269513314467901068389032033271226/2197"
    ],
    [
      "-9777809863251923573",
      "166649880301853240137109881122"
    ],
    [
      "73883603455659781013/4",
      "544893994239027865371642446271/8"
    ],
    [
      "914657760276408779622254/44521",
      "649437151191045483451191264986300991/9393931"
    ],
    [
      "5948265194483548551976847/208849",
      "-9863050989027549183604799657196608190/95443993"
    ],
    [
      "-25143722977897107697",
      "171261568023206228150840746830"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -250/51 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -15108348426986418946992T^8 - 165645727401183163968960T^7 - 386516497356749936802240T^6 + 804907699137855510269760T^5 - 423101056239642087896040T^4 + 2012740403434408357952040T^3 - 832891923170874739577340T^2 - 2371900038780270082074480T - 881248331824987560372900,\nA6 = 717503217218577271350459150984576T^12 + 11638864686052244686069138775512320T^11 + 58135061140664436934300824832212480T^10 + 62512031622436328327919258342862080T^9 - 268895690113423321891997914072476960T^8 - 870815838806588886732350721838471968T^7 + 2170770437820474859902147687346459920T^6 + 114853264658855014380401497670938080T^5 - 2228934495975748087928517866419014780T^4 - 844990471869666800949969469071688800T^3 + 1481780271644919349838123819347167336T^2 + 1307631772289943212553000319429645920T + 318018311456252316549507444881168100.\nIt is a 2-neighbour of another fibration built here: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-18 18:29:50",
  "updated_at": "2026-10-18 18:29:50"
}