{
  "id": 4220,
  "curve_key": "2422935260336331730387219038861824823825:-124136933758342631817455323263542311345352943254966332565625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-50477817923673577716400396642954683830",
    "143677006664748416468007560110018291819554894594727481797"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 272.13747112294544,
  "faltings_height": 20.605328728294502,
  "conductor": "91845577056807951694322697837878934816027414415778863367584405899332338321985650038450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "23",
    "29",
    "47",
    "59",
    "73",
    "97",
    "241",
    "367",
    "2832287",
    "44870469257",
    "416713987128255161",
    "10300394492972934361302585228509"
  ],
  "discriminant": "-686260168613455500972898141221570848955361986552665769620352183612024142080232816781348483284964812942239744000000",
  "regulator": "813980174066564711182061.29554247208719573943227063582365410320272198006676060702662166",
  "points": [
    [
      "1506024575133016489",
      "-8430421212246179046705327445"
    ],
    [
      "7165888759087265869",
      "12244455558114743467442370515"
    ],
    [
      "3424137956171178139",
      "3313767595577215130785184705"
    ],
    [
      "-4966967544826333511",
      "16488171309818521530880172555"
    ],
    [
      "5618450972817430633",
      "6117798180765633803165355371"
    ],
    [
      "2647204251992306569",
      "-5348149225283893367145796885"
    ],
    [
      "-11292616986686933053919/1849",
      "1190366168174551994313962247264305/79507"
    ],
    [
      "30946507026060565033",
      "167983959284307502442634675371"
    ],
    [
      "-8177968677974126951",
      "-3089862326588594417536364725"
    ],
    [
      "45096680592210203239",
      "299300672111036551974020074205"
    ],
    [
      "-6161516419139636951",
      "14858645560558164503850735275"
    ],
    [
      "1267353073661678569",
      "9040983959097836041490990315"
    ],
    [
      "3739943337606114499",
      "-2684040640074211074298204375"
    ],
    [
      "33108290181854335969",
      "-186452109167128090072768508485"
    ],
    [
      "1622449485435444674449",
      "65351057445047606029200605097875"
    ],
    [
      "-5469717006355874111",
      "-16004201438293117033389158845"
    ],
    [
      "4481479200086034889",
      "2732435065001324186021790155"
    ],
    [
      "20171373818355448469",
      "-85632270948267947046288184985"
    ],
    [
      "5564667304223717819",
      "-5924320441291830523978715935"
    ],
    [
      "14975444154858155071/4",
      "21422802247893133780078601575/8"
    ],
    [
      "2375524262587709572849/121",
      "109106687925795750252657938048065/1331"
    ],
    [
      "1470469077997949993",
      "8522353027951557742525840171"
    ],
    [
      "583586287446770650849/121",
      "4689278495295274761343411029265/1331"
    ],
    [
      "363770800274055073609/81",
      "2004477520805778771721681994195/729"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 153/172 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -46899334113383125285632T^8 + 270055671557662617610752T^7 - 110499855853494623134464T^6 - 1097978606080292495697408T^5 + 798354426662958846861720T^4 - 652775607268414350434100T^3 - 1472431025874707052625953T^2 + 2703862379229266288830500T - 984764302175595161629827,\nA6 = 3885040300642071987577481657671680T^12 - 33785823226478031065590325732302848T^11 + 71535134823792731310067418119643136T^10 + 161716991851894171424472252351774720T^9 - 720321276317174942738930961334015104T^8 - 173535940015248246031810704538019520T^7 + 2662884349300283514864711968426262768T^6 + 18543461312481910222042123064099856T^5 - 4146251221815493809167896322067912459T^4 + 1352969495572413131622726277427086950T^3 + 2682293599935058314574939466346897591T^2 - 2185595594424745389481946472892633500T + 480683366018569365299225874952658046.\nIt is a 2-neighbour of the fibration given in curve#4205 (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": "2026-10-14 09:11:13",
  "updated_at": "2026-10-14 09:11:13"
}