{
  "id": 6127,
  "curve_key": "2084084084420201658159549361216:-3290206855588724317258298473802425747450427264",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-43418418425420867878323945025",
    "3808109786561037988151394670153211463827077"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 209.61455924314396,
  "faltings_height": 15.432771610878515,
  "conductor": "23354182517806638348389168280218084681450183982791012291203885349473113960",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "49293430093",
    "521476916652319",
    "17728310468531826294756873440508535824823"
  ],
  "discriminant": "-1026294475881151602837448895107916439936527055998771574649983863078309552464536492000000",
  "regulator": "1653133047492139489049.985581625998874570379505463744614697793993886419584473667315",
  "points": [
    [
      "252981952688357",
      "-3002473178356395902886"
    ],
    [
      "564050527716461/4",
      "-5597363972953433651775/8"
    ],
    [
      "633885950437324",
      "-15198302022819479185965"
    ],
    [
      "8739619212093169/16",
      "-765504088456941544617375/64"
    ],
    [
      "161586223736557",
      "1005646666286970112314"
    ],
    [
      "84845581034197",
      "-857340593600182664154"
    ],
    [
      "-201821231113596",
      "-2085743163019258178695"
    ],
    [
      "-227348909524091",
      "-1388573745353494371750"
    ],
    [
      "873351390264609",
      "25140225302277606698450"
    ],
    [
      "3126356745071533/9",
      "149460353004031467118462/27"
    ],
    [
      "372723614079709",
      "-6277330843732597371450"
    ],
    [
      "1006043802688908",
      "31278882500690037066035"
    ],
    [
      "2733536168855709",
      "142515633834372101717050"
    ],
    [
      "59446446794809",
      "-1198797604806666651150"
    ],
    [
      "-168794720807051",
      "2515485675481597104090"
    ],
    [
      "-39286657456791",
      "2335216834224021470450"
    ],
    [
      "17535067408933",
      "-1747042229159779338150"
    ],
    [
      "142633064035809",
      "719000710968337629650"
    ],
    [
      "-126705662452841",
      "2697275548479128048250"
    ],
    [
      "5089495068589",
      "1894007337125803548870"
    ],
    [
      "-232627526087311",
      "-1148764046647525115730"
    ],
    [
      "-217447119905396",
      "1722705227687390210355"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 191/42 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -135905733791177100879168T^8 + 1170105215005157329310976T^7 - 3263768771352480615865392T^6 + 2346518634849035692218000T^5 + 245936114819649867667320T^4 - 1432517413140009535585824T^3 + 956236108008185762686704T^2 + 156236369911740531083592T - 257526183060059049073467,\nA6 = 20737642716792465943326120257995008T^12 - 244496554556977289037909247323669504T^11 + 1157988470380485097232050906009638528T^10 - 2790680074288331258566479141986856192T^9 + 3101966268250480126177717673389002384T^8 + 656755301509986568870676405232297792T^7 - 3435411333307752838327381281470537136T^6 + 658445704499369672945800020331508016T^5 + 1474214217968126497120054729756719768T^4 - 229935451360122136801662723346458528T^3 - 405994673197848668282333146509853248T^2 + 15664520646757240102474163329610664T + 58525848665960980471096021479565974.\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": "2026-10-29 07:47:17",
  "updated_at": "2026-10-29 07:47:17"
}