{
  "id": 4236,
  "curve_key": "2685793700308565617497856832572196372425:-136938981037191300640223430393095319426425404112327846414725",
  "ainvs": [
    "1",
    "0",
    "1",
    "-55954035423095117031205350678587424426",
    "158494191015267709069669837780824619213169697758645314648"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 272.36638474912513,
  "faltings_height": 20.583667935117507,
  "conductor": "31806969506801151852156648388722049730308181927719591097449259312127947925467681356373925674035950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "101",
    "151",
    "448175827959916799",
    "2276177021370588202448759",
    "149774147356843215069689409757982345350847837533"
  ],
  "discriminant": "359754377688695765544584966027922965049761109507365404128287453939552552718903079704976545973219710860523009292500",
  "regulator": "886518569677594013036404757.7576377162040506554848688466363176115146335938292095890962329",
  "points": [
    [
      "24974263163442869543/4",
      "57981448963765348917127677993/8"
    ],
    [
      "4759746197858435282",
      "10437094139228094426979641"
    ],
    [
      "4934121026525872862",
      "1591885663812819312482430636"
    ],
    [
      "547091065515200098523/4",
      "-12777692744432260034523202706817/8"
    ],
    [
      "-1789975632834945148",
      "15903315573526485962625421131"
    ],
    [
      "25018057848866236967/4",
      "58350067947972302953232897481/8"
    ],
    [
      "26442670344609186257",
      "131026817584393758848186994651"
    ],
    [
      "23124912488207197502",
      "-105975830757326009789243590059"
    ],
    [
      "13380127126348754543",
      "-42488078718555495391734387633"
    ],
    [
      "96875812084255972757/16",
      "413149523824358915925297657759/64"
    ],
    [
      "49203023012114864027",
      "-341354403423026298085020054519"
    ],
    [
      "-8132374798040366284",
      "8700261127048716610518526416"
    ],
    [
      "10555109984431371182",
      "-27273460672281451610101955124"
    ],
    [
      "1729269600408284828216/361",
      "-4225058786879159960631020937672/6859"
    ],
    [
      "638947973521285962671/121",
      "4265515750278886356778223871027/1331"
    ],
    [
      "246798900468143439527/4",
      "3849888262049326285572853630641/8"
    ],
    [
      "4760361837356792711",
      "-86655117727875873899565183"
    ],
    [
      "-2253530389445322034",
      "-16527068198949592767844619508"
    ],
    [
      "4924128132236186897",
      "-1537814145745539382093377429"
    ],
    [
      "-192991568056801360696/25",
      "1427416402565561241623202339123/125"
    ],
    [
      "43809126068561862143",
      "-285984970236182396462905501311"
    ],
    [
      "450160966379818932233/64",
      "-5440565565899095046836340873553/512"
    ],
    [
      "834511668837892619788/9",
      "24031132857856935108002140145057/27"
    ],
    [
      "-5138378672818647115663/3721",
      "-3465670406407100220887043959755389/226981"
    ],
    [
      "3217671585849796952",
      "3430212191842674479612298216"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 970/479 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -11140892170449903078832T^8 - 78517047092297850338880T^7 - 410980750922999091180480T^6 + 1172978174531038105951360T^5 + 202359376870041611948760T^4 + 727464198947794396860360T^3 - 533980972281075528757060T^2 - 2994527120513758550219760T - 1424568869019231533236800,\nA6 = 466667176236662985209696435215744T^12 + 4902108138265145170676233713437440T^11 + 30904617405388839778675659644720640T^10 - 2235477311686016201360264232122880T^9 - 1928619458298746783809833278130720T^8 - 1321657250248806493665223528336049184T^7 + 1152166039831051025589342359093195760T^6 + 3336273056288691191096244581228211360T^5 - 1565104306692700007697832976891694060T^4 - 3952505302344716290555441880536817840T^3 + 26850110070164475305157052575243376T^2 + 1903147075480838773866179023498043520T + 656146040532506595230072169941913600.\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 04:40:46",
  "updated_at": "2026-10-15 04:40:46"
}