{
  "id": 4265,
  "curve_key": "175339122096703713656294546004377854225:-2326091540346685811512954954370982771109542323454963852025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3652898377014660701172803041757871963",
    "2692235579104960429687437813918897222945718176444904017"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 264.1830794184956,
  "faltings_height": 19.811837438168418,
  "conductor": "187379184918627485277279847733750785346305832188682174179917091245277597430578005994654650",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "59",
    "67",
    "151",
    "6558883",
    "28798873",
    "63900859349050932242093",
    "63815270023316305769399368949867003161163"
  ],
  "discriminant": "-11637497363592017416985934095128842755189390620210075178712696919847364014368917553289946253638013508152320000",
  "regulator": "22748363104840810922559183.60294860684563129478819257455958074103236567929151490423649369",
  "points": [
    [
      "1142049976083013158",
      "99969507698260461096168225"
    ],
    [
      "1140330748831843862",
      "97760600640963336247918529"
    ],
    [
      "-1996669794612390858",
      "-1423293149148674222638709631"
    ],
    [
      "1077445381045048022",
      "-85035878481432890267080471"
    ],
    [
      "1748562572028066252",
      "1284948898000132622168234259"
    ],
    [
      "-1906736959137543768",
      "1650797276690147569742755449"
    ],
    [
      "49609452355003470222",
      "349163552139969950590684480929"
    ],
    [
      "4865032674700084083/4",
      "1762893178284799749413357247/8"
    ],
    [
      "855143728894221102",
      "440254557695811466118938689"
    ],
    [
      "1083623427640235502",
      "-79391456333220306071414511"
    ],
    [
      "5707984858373401182",
      "12954301285515584673754284849"
    ],
    [
      "1256816144890565838",
      "-294047859737673631409794335"
    ],
    [
      "26825074541518692744/25",
      "11215951541167473182753543637/125"
    ],
    [
      "1099468843349943942",
      "-71136895931690856578861031"
    ],
    [
      "-612448414140890034",
      "-2167884278750929484932039071"
    ],
    [
      "13439746704598563663/4",
      "42595503738405236673414759657/8"
    ],
    [
      "1136340994128112746",
      "-92851564399160301811542195"
    ],
    [
      "1742293456447524702",
      "-1271494049205345067556112591"
    ],
    [
      "12202033385612358456318/10609",
      "121324449684165061935076195748103/1092727"
    ],
    [
      "1826434325378163222",
      "-1453681564291119860135578071"
    ],
    [
      "1083109737263889342",
      "79816869484075995022166769"
    ],
    [
      "-1722665753418944034",
      "1967946832464107687138829105"
    ],
    [
      "567485861020060127091822/380689",
      "175680266743856442972329085424453785/234885113"
    ],
    [
      "1049141000299031262",
      "120897906950414320000249329"
    ],
    [
      "-944862567919172532",
      "2302212421659292279695823905"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -765/779 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -43748288271748043306667T^8 + 231005568889113088943880T^7 - 41811485832351502958160T^6 - 845807620575605275473120T^5 - 1273696848822391714464840T^4 - 2479538071066771770038640T^3 - 723198327599392266394800T^2 + 1473487148401141809248640T - 304202213366895598996800,\nA6 = 3496542619563277295766359856805926T^12 - 28800862572418754868158883533967960T^11 + 61983572330491650413223232787176320T^10 + 92074250730656596945854018024980640T^9 - 554403246688053294582105340433199720T^8 + 21665370800800153534189468438161072T^7 + 2696996106708736152461893481712643920T^6 + 2003709311601233451889158133572553920T^5 - 1216187330113512252280500336077191920T^4 - 278472048982945948218206647760751360T^3 + 596780792582732967834659478701644416T^2 - 397452607403627859574187730447221760T + 82758424296652691415712452035078400.\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 22:28:44",
  "updated_at": "2026-10-15 22:28:44"
}