{
  "id": 5959,
  "curve_key": "1791665125278484008545142241:-75937410975743722879729542294356816003665",
  "ainvs": [
    "1",
    "0",
    "0",
    "-37326356776635083511357130",
    "87890521962663235395881509917064812836"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 188.26145617593215,
  "faltings_height": 13.471898806432645,
  "conductor": "742709177144117005880487154251701674439611276723465632190074114",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "23",
    "6343719157",
    "11585937836827",
    "391582211890560968658077746441976321"
  ],
  "discriminant": "-8756254791237344891621868589251221559610661430120387524734895531097062227968",
  "regulator": "2096506103521536897.54371925813558178092115210866755965901588841580726023326798",
  "points": [
    [
      "3984910829828",
      "-1557810452537614426"
    ],
    [
      "3661374931780",
      "554890802239609366"
    ],
    [
      "3292815210956",
      "827349681537913838"
    ],
    [
      "3631487076332",
      "480930586478844494"
    ],
    [
      "-87379099660",
      "-9547324097797061914"
    ],
    [
      "3509865229436",
      "-344400073178308474"
    ],
    [
      "12014807760884",
      "37065157833299803430"
    ],
    [
      "3474998243432",
      "-379779264751605646"
    ],
    [
      "3609820071278",
      "-433518685780873576"
    ],
    [
      "3910603580564",
      "-1313811521479603354"
    ],
    [
      "186715515592904/49",
      "-340709767572657538966/343"
    ],
    [
      "3576259036388",
      "-375270276766800346"
    ],
    [
      "-5979948060556",
      "-9861973325867303194"
    ],
    [
      "3711521276882",
      "693257389100848634"
    ],
    [
      "3468885863390",
      "-389027320204671814"
    ],
    [
      "3399902798132",
      "534007896684914534"
    ],
    [
      "14540645844620",
      "-51180818974827648466"
    ],
    [
      "-7055599387852",
      "-110191607958266266"
    ],
    [
      "8855508288896",
      "21255485680246116038"
    ],
    [
      "-1335164841964",
      "11633882623713480038"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -5/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -70456322121395744118987T^8 - 270736805521800700486056T^7 + 681665761636047060624T^6 + 1234481960342872464204384T^5 - 427072536207795566991240T^4 + 932522348198042719391664T^3 - 991232578762048531399536T^2 - 1438822739314664423398656T - 343540998025511181060672,\nA6 = 7048126807600643691644744903627910T^12 + 41401267256924276544233395256738232T^11 + 51649295889445830016007199603753312T^10 - 208657301544441260965791912828085920T^9 - 522635766473158675684276944285342504T^8 + 252396058528754737573291576653064464T^7 + 2238764228696773065046286671966044432T^6 - 1352643968572944143440516173662043456T^5 - 2058834580016599491043353648535363824T^4 + 387649811099219784510189392096797440T^3 + 1175036907274176750041024493365538432T^2 + 525410171790549433434615584174902272T + 77513965269216205111736833614792960.\nIt is a 2-neighbour of the fibration given in curve#4187 (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": "2026-10-26 21:59:45",
  "updated_at": "2026-10-26 21:59:45"
}