{
  "id": 4271,
  "curve_key": "1375409219890994173190229177424316022241:-55671809404645732983834564381338100706339155465584422188625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-28654358747729045274796441196339917130",
    "64434964588710339099272512212386122044622467244731421476"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 270.5336484093133,
  "faltings_height": 20.508311061830753,
  "conductor": "142812942445508923720029062042844910500196247032039142091471085180891501774486242387443517965718",
  "bad_primes": [
    "2",
    "3",
    "11",
    "41",
    "43",
    "59",
    "197",
    "254446487",
    "604144748177",
    "686934957628451414261516772217020236649116052535593064108107428873"
  ],
  "discriminant": "-287858363699738731464006152638883655726913414090345095048838607041309796431041765635891330606758440983096382240768",
  "regulator": "332167987236783109646676482.5860059599029533437128973737758069068768776782492670726612185",
  "points": [
    [
      "718506088253287252",
      "6649628775686730458924639014"
    ],
    [
      "-3718210555020294740",
      "10934958125611625288707864846"
    ],
    [
      "-1496286526370663630",
      "10196082554770854306302807764"
    ],
    [
      "-3041056267557444092",
      "11110838082789717785314226854"
    ],
    [
      "63369510481644156724/25",
      "355508100672456584231476814222/125"
    ],
    [
      "-20256337843882274717/4",
      "-71408619037814654730912719293/8"
    ],
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      "73904629755869640376",
      "-633723931374378802837696694042"
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      "-5489044628822350700",
      "-7505813709433337407926976826"
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      "5004924827877463300",
      "-6811151086166219919359398826"
    ],
    [
      "6788730079381200148",
      "13519596279765745727832292678"
    ],
    [
      "18085309082078459551/4",
      "41804124453258986495645372393/8"
    ],
    [
      "185077141972999979659/100",
      "4212106980503335054394183850403/1000"
    ],
    [
      "4830836265454637746",
      "6224754914876327094190999546"
    ],
    [
      "-55507599207170983664/9",
      "69154101404401936772652968110/27"
    ],
    [
      "2731721450822745634",
      "2558157307278100583703570340"
    ],
    [
      "4837129550609654320",
      "6245671839119281444718421766"
    ],
    [
      "-152196694060550899364/49",
      "3811331546284704800648351891698/343"
    ],
    [
      "2084528997288245398",
      "3709709654524485032825769178"
    ],
    [
      "-142979935085624122376/25",
      "-802772721113084811426778924978/125"
    ],
    [
      "-13696826060439552793004/2209",
      "-200346901620949668166405925635270/103823"
    ],
    [
      "7374022972574736148",
      "15940781721682009125957835174"
    ],
    [
      "4217391092928645178",
      "-4312827381172778823156138836"
    ],
    [
      "10558841286668419888",
      "30644316923766341920858358218"
    ],
    [
      "369140023761405298270",
      "7091552368495845524654203808314"
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    [
      "7688962410127709524",
      "-17282512381147870634996431994"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 19232/633 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -9801785533668367408277499T^8 - 121843241966486333706286824T^7 - 383434732762042957835672232T^6 - 85754468638713501529031952T^5 - 584201627367901316547607440T^4 + 1235140044591109335942134016T^3 + 994771523582906627448194816T^2 - 550790635100880788122728032T - 647714191600162651688347312,\nA6 = 12142329458953725303990225302566830294T^12 + 247791101750863056653001398463488667192T^11 + 1886090538602583189200926091842195641480T^10 + 5912076790668428510577901681319655809040T^9 + 1282952245208814516295621371483268940160T^8 - 25791045529140834460411754210526102555072T^7 + 619130399100809058015628676691838434624T^6 + 31601519751505535243254509940106610677280T^5 + 10405299225003196422075679041028274690640T^4 - 27172444692997266799042742904489658895040T^3 - 13432438015701644454859263568215615214016T^2 + 8212424024664720375926323815936672405632T + 6370397708074310285430666560056789129600.\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": "2026-10-16 03:07:03",
  "updated_at": "2026-10-16 03:07:03"
}