{
  "id": 5963,
  "curve_key": "1300382709400877339287061838312442321:-1492071793880320489400628117735892564695637594161027865",
  "ainvs": [
    "1",
    "0",
    "0",
    "-27091306445851611235147121631509215",
    "1726934946620741304919044043558537680283616709134681"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 249.47952128305016,
  "faltings_height": 18.634362128248885,
  "conductor": "3160766107543915573005279846610883009909959037472309770941987988415496938",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "43",
    "47",
    "71",
    "120629968427",
    "197027661082697",
    "414677700574817585493790585579583"
  ],
  "discriminant": "-15820214210325146503563031719148910017470260514683647213306318572090856697650778255460548677421764313088",
  "regulator": "120886865519781707273.0417259857074429957884243159855390190777530136732005995665588",
  "points": [
    [
      "81643843220607878",
      "7701385243976555829699533"
    ],
    [
      "101643282171296894",
      "-4837215847480877026800739"
    ],
    [
      "-35356400047183642",
      "51386650642846370214697229"
    ],
    [
      "515058096288668870",
      "-352718647626762044275161619"
    ],
    [
      "85342364315464466",
      "6039410375745716373486341"
    ],
    [
      "103228892756525018",
      "-5509768625434944190624591"
    ],
    [
      "-131534785002107914",
      "-54905812287373264862154979"
    ],
    [
      "41964424074460838",
      "25767494343513655719235469"
    ],
    [
      "952494537660063286/9",
      "181472456655144737660278687/27"
    ],
    [
      "109183972991906750",
      "8402136492792606690940709"
    ],
    [
      "863170078341056150",
      "-788326239347530150831313491"
    ],
    [
      "95917920266977382",
      "-3295720650117131567717491"
    ],
    [
      "93977618032683686",
      "-3308978365726782093910579"
    ],
    [
      "60183463908915830",
      "-17733407990887459027169299"
    ],
    [
      "99068738496627382",
      "3918534684920344216032109"
    ],
    [
      "20600311197748646",
      "34315999396219234357055693"
    ],
    [
      "302966747779777382",
      "-146041567471922190092501491"
    ],
    [
      "74914429019128454",
      "10855313383034825767511981"
    ],
    [
      "187271769857927510",
      "56756083775134321246966829"
    ],
    [
      "1290494734014916640",
      "1454622134004291203004165371"
    ],
    [
      "108856153469109469262/4489",
      "9903478050949342136512208240519/300763"
    ],
    [
      "105133896811533254",
      "6385891985915076988857581"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -159/26 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -1372222876353130936512T^8 + 45268756700642132762880T^7 - 453891857520504970746000T^6 - 18572366977872800377824T^5 - 1977700547530427488113780T^4 - 1507927812614917602109344T^3 + 3528535081023240424639497T^2 + 739749873585389019295698T - 1838633851571299960339827,\nA6 = 20363691452208588844425836248320T^12 - 988378436168557724966091861408768T^11 + 15965030664200057535359388315912960T^10 - 108360266161421346549906270794042880T^9 + 467598254108283083435022152559186336T^8 + 1192549643051435746625317280337017856T^7 - 1110484823304716478646019257293024192T^6 - 2091654238173550372318136090501079360T^5 + 2721622409681114022374952201370443921T^4 + 1932785120958781428078049659343305420T^3 - 2684653676111216975923215434658050073T^2 - 583595531728434724891836911712239106T + 959603028788038989675020832528690546.\nIt is a 2-neighbour of another fibration built here (itself a 2-neighbour of the fibration in curve#3900): 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": "2026-10-27 01:04:09",
  "updated_at": "2026-10-27 01:04:09"
}