{
  "id": 4187,
  "curve_key": "2199946750505012236314486258058857203761:-103077123403522691601670964699345975281199979160568771300009",
  "ainvs": [
    "1",
    "1",
    "1",
    "-45832223968854421589885130376226191745",
    "119302226161484596742096486192775906838936727112415905407"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 271.7677553475697,
  "faltings_height": 20.42250307233648,
  "conductor": "23245678877229473722476726532968739564574826882685018334849453662724503354377590572824690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "29",
    "79",
    "131",
    "7998297600445324621",
    "872091769630260208978461227089207530645161142854134055377"
  ],
  "discriminant": "12924460012696074420095146791118469958548390890119320909042371598602360653011015688790990825180995190172160000000",
  "regulator": "10484040136577878626124740.96824913182185286289286047218641691479598118493762814546447605",
  "points": [
    [
      "4849152048724378047",
      "-3328528365654842802704537024"
    ],
    [
      "-620327327803177153",
      "12144731430424878176911331776"
    ],
    [
      "126143163082372444047",
      "1414758001189315967845145106976"
    ],
    [
      "3804186060982898047",
      "-38191543753182994952881024"
    ],
    [
      "2546033700748515247",
      "4372180468205076680387918576"
    ],
    [
      "3433025740283185547",
      "-1555479146957666879326893524"
    ],
    [
      "5495786360368065924093/1369",
      "-4289449832264122329120183108422/50653"
    ],
    [
      "3546515776226775935",
      "-1168244519334703932664947584"
    ],
    [
      "794694589045453962279/25",
      "21931278458184478075218828808448/125"
    ],
    [
      "4076474056291704447",
      "457968915598407006339381376"
    ],
    [
      "-102141767600716716186473/48841",
      "-154922994667822050893574927262693664/10793861"
    ],
    [
      "-4153089581755554753",
      "-15427716394030408235548591424"
    ],
    [
      "-7615761992743460253",
      "5161068599207629302218059576"
    ],
    [
      "4053633543656633547",
      "-352517746940309402336372024"
    ],
    [
      "4093945363526008447",
      "-532654398283642392649594624"
    ],
    [
      "3416544009286592927",
      "1610887480991751273086181056"
    ],
    [
      "4012303473974275797",
      "-42659469353683898963561774"
    ],
    [
      "5402531835896069247",
      "5420126003709845059557890176"
    ],
    [
      "4556436219606167661",
      "-2251066209812062633631208566"
    ],
    [
      "22211849577519808215",
      "-100298858190310380200630350472"
    ],
    [
      "2831626321792881377",
      "3496681137962638512873350366"
    ],
    [
      "-4498562880368581953",
      "15311552659356456077526078976"
    ],
    [
      "3768320657057186687",
      "-320577157163222399689416704"
    ],
    [
      "4310872334417932047",
      "-1355350282864435030755839024"
    ],
    [
      "1211455858138450076863/289",
      "4498074710032854938742610946368/4913"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 1815/788 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -28627871103769984370352T^8 + 250727503810391437739328T^7 - 288854657346414564166464T^6 - 1046563569239575640345856T^5 - 2237723908977579748622280T^4 - 2929539083122814891913864T^3 - 75441235775660299609524T^2 + 875991646929384189258912T - 320782968880211172761712,\nA6 = 1174522160214039703024876049652096T^12 - 16131442871155893431215736050050816T^11 + 93303642018533859944970389927921664T^10 - 231262072230896017869661906694261760T^9 - 366595866204221333220660871885856160T^8 + 1809536503795113401754131369092034592T^7 + 3099112034539070371703903967203738928T^6 + 554652868729364853437329955292672288T^5 - 394633275566228428167096479633610540T^4 + 857804045527423469286999564571793520T^3 + 199633165297674561155987038442283696T^2 - 284106783901779659207593408557902976T + 70103120599376154084348899681491584.\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": "2026-10-11 23:33:53",
  "updated_at": "2026-10-11 23:33:53"
}