{
  "id": 4214,
  "curve_key": "16706799497371227370375551888147526337782449121:-3263633111415075244823632839922676457222915029689599478018630424416081",
  "ainvs": [
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    "0",
    "0",
    "-348058322861900570216157331003073465370467690",
    "3777353138211892644471768263568785185627152160140934324917967304100"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 320.1224248855643,
  "faltings_height": 24.706953412734563,
  "conductor": "942939644904828574080077075792115067906593731930478571634760145916894965223947101427947162266137817956890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "41",
    "47",
    "59",
    "79",
    "217754441",
    "385955269823142789727961",
    "1808572461127438133859688103976516527025876422170296677229023"
  ],
  "discriminant": "-3465362751078331218348813958919756738988424519330973721318190120787291282742763596067470683157328350788259522439408269553226315366400000",
  "regulator": "215580745635293414559483426850.10475154960005974175334551447344729906607728747817145660150353",
  "points": [
    [
      "-9364256772650191799720",
      "-2493093555803296785300238674853790"
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    [
      "12825770080399858494580",
      "-1192929647124812497286791867618490"
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    [
      "-14240692635183276626060",
      "-2417844150472849589859709061291450"
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    [
      "-68142897500178114703805/4",
      "-17458963316494254798642044351851045/8"
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    [
      "5346977160729859835395/4",
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      "-1491097421323012812868995904973930"
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    [
      "-6640066355018532723620",
      "2407430118749239785017032758385510"
    ],
    [
      "24672344755898367144421780/1849",
      "97662791611095721111852130162650569970/79507"
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      "-1303611254383554355098362532650240"
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      "-1364720323205887699985443882356890"
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      "1201606045811175435809490974170822"
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      "-22431050673495160627340",
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    [
      "24351237661691565357400",
      "3121148297868796031784188788090210"
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    [
      "-42283523521179196980995/16",
      "-138434192887091383563002263432252535/64"
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      "1547933697062601961780",
      "-1800636258015505532444953800826490"
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    [
      "-1069538304893370937100",
      "-2036760022424706505255227163255610"
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    [
      "16162657786394896744180",
      "1540779355457823391411695677053510"
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    [
      "22262357427477509895220",
      "-2657490971940693218749142406639290"
    ],
    [
      "-20611908029920955695280",
      "1481389428336586690298979893194570"
    ],
    [
      "8640486078471729623380",
      "-1189555148722598152578544685208890"
    ],
    [
      "-22391971859918630038220",
      "586277730660860968845401015864710"
    ],
    [
      "-788081766441375048600830/49",
      "-783285462520149019105792665394483370/343"
    ],
    [
      "1004505328532386247699800",
      "-1006593821715591130743472723231215290"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 2617/2100 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -123856789139706169159947T^8 - 444860715403915335809784T^7 + 386197275608827081416504T^6 + 1527252937315431153244272T^5 - 1375436505233375995520880T^4 + 1122976665942695182127232T^3 - 920913248897305236746496T^2 - 558254638916475632295264T - 66664274811511860464112,\nA6 = 16359416402689331569871278519529286T^12 + 84307064804680497817942655822018088T^11 + 43582982500411768342190410573462056T^10 - 406313301062273227318175674455353520T^9 - 696574825662812869066591591106450400T^8 + 831815699985675007793533243030026816T^7 + 2339654226324227927870456252492273088T^6 - 2418192605459673378876521710121559264T^5 - 588423094738870081007533655250779760T^4 + 462827873819015983743769059572260800T^3 + 312326563016748800922506015981603904T^2 + 77162055820545612135770412695494272T + 6735862148389763480692013144006784.\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": "2026-10-14 04:04:51",
  "updated_at": "2026-10-14 04:04:51"
}