{
  "id": 4253,
  "curve_key": "1407975519602911211043583670297555690641:-56274133460251260734065813100474210798328004117383242965561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-29332823325060650230074659797865743555",
    "65132098912327848069391029885497504608521560893445497025"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 270.5551705780549,
  "faltings_height": 20.494794219370984,
  "conductor": "54275045947234878747477255115920299904009892715164363090991870522074318653843577009641023336490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "31",
    "6713479293533197433",
    "4153367585118333162290315570397757229716047436670281272008366959420097"
  ],
  "discriminant": "-217369430954043749029798024293302595528576395190366834142287100502119500730979156510801059456761115990584960000000",
  "regulator": "270279687383918662328170741.6898351820211644842515795654985213954187906682280520242857961",
  "points": [
    [
      "29179822216090424510",
      "-155095828551921779443322431255"
    ],
    [
      "-2669663263862820958",
      "11154097792511857930898562641"
    ],
    [
      "4680301338572967830",
      "-5510778534338373133419386575"
    ],
    [
      "-5722421622901595890",
      "6752765202638050436988844745"
    ],
    [
      "182483260029464629790",
      "-2464027297902922903327692395335"
    ],
    [
      "9029414753462891215/4",
      "25824288151673692768264624985/8"
    ],
    [
      "37829807705494820270",
      "230420270663004944289929048585"
    ],
    [
      "1594072666193706260",
      "-4735408487448792662266307005"
    ],
    [
      "92064572454860865710/121",
      "8753718749219145269226524727595/1331"
    ],
    [
      "7799207529169735310",
      "17628576095794494822523883945"
    ],
    [
      "-1069345810300799316850/841",
      "-244345101816663633514055212746995/24389"
    ],
    [
      "-6288084150024392890",
      "973908994385251948006459745"
    ],
    [
      "-6030924427169022490",
      "4762253476932777795935935745"
    ],
    [
      "3119210330560031150",
      "-1996278121940916944682110455"
    ],
    [
      "84446582784164650526/25",
      "267836187793975377752292983461/125"
    ],
    [
      "3786962564249327486",
      "2891184678434425304474792297"
    ],
    [
      "294318383680705670210/361",
      "-44323875785379893848294376539045/6859"
    ],
    [
      "-3913316230981181614",
      "10954086722554167097762669757"
    ],
    [
      "-1397014537601174938",
      "-10167792121355267295966353383"
    ],
    [
      "10226654585608588010",
      "28891255336802560947639444245"
    ],
    [
      "195377007639450936479928590/29343889",
      "-2041796732445637765955955706152471978815/158955846713"
    ],
    [
      "3926323385674944934010/1681",
      "210877220121397602620463242095645/68921"
    ],
    [
      "4005915932395875710",
      "-3451327218225251234035567255"
    ],
    [
      "734635657111874646706670/116281",
      "-455533973905590579634959559528024955/39651821"
    ],
    [
      "23663923139261938970",
      "112349258459671551972527288645"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -469/370 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -6045653798989791126192T^8 - 62415704538217319360448T^7 - 1599340192212345051878944T^6 + 411285604330977976052256T^5 - 987166911410498278789680T^4 + 1046627474370060703109584T^3 + 194010634771867183414656T^2 - 729479896920873105811452T - 225965831905541594247667,\nA6 = 163989304706795551092980878190976T^12 + 2463417736840188795628573229020416T^11 + 99064787504796030904023011794321024T^10 + 306093533334403679180135432179319680T^9 + 1458791938240704239622260678224652160T^8 - 2067052078435764908208365147286526272T^7 + 225696680714681572698300960927997248T^6 + 1453625359670481930865233085816499472T^5 - 247522312386237949189300655828535660T^4 - 553746777745423527483394159931837640T^3 + 133678131457935919739674847770663476T^2 + 203231717596297497476228246857348516T + 40705869704413231155701476152234574.\nIt is a 2-neighbour of the fibration given 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": "2026-10-15 19:48:22",
  "updated_at": "2026-10-15 19:48:22"
}