{
  "id": 5562,
  "curve_key": "18992086037161490922121936:-75070206117536995262281073574408405184",
  "ainvs": [
    "0",
    "1",
    "0",
    "-395668459107531060877540",
    "86886812635906299474604287764902400"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 174.61819379967974,
  "faltings_height": 12.521702400842214,
  "conductor": "978646144247239614110790412280250565651034498850939480",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "173",
    "10900501",
    "52151137",
    "1168186246921",
    "181551254158072233739"
  ],
  "discriminant": "703065336329162618996086855228387967176117962388343651873953533309600000",
  "regulator": "11399493668711430.473782243045131131661487440462795618293936978024049768808",
  "points": [
    [
      "451932611120",
      "-19376363906641800"
    ],
    [
      "2478645412820",
      "3786050302323026400"
    ],
    [
      "455118670250",
      "-32875629533210070"
    ],
    [
      "247566038210",
      "64076521774583790"
    ],
    [
      "522125616934",
      "-150457744400626170"
    ],
    [
      "687985547570",
      "374583476222776350"
    ],
    [
      "675360114560",
      "357361841847555360"
    ],
    [
      "1816044545195",
      "-2314666819111874400"
    ],
    [
      "2103397639595",
      "2925860941273654800"
    ],
    [
      "-55270084565095/1024",
      "-10772933042325724337475/32768"
    ],
    [
      "767826695780",
      "485551491898406040"
    ],
    [
      "-704865917980",
      "124809004514507400"
    ],
    [
      "250338883940",
      "59365302004975320"
    ],
    [
      "99154268720",
      "220520833375534200"
    ],
    [
      "2935589023970",
      "-4921721468355726450"
    ],
    [
      "-406478172880",
      "424920286691065800"
    ],
    [
      "-398027558305",
      "-425812017642627150"
    ],
    [
      "89104511870",
      "-228775923466303950"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 2/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -129423262682594003679387T^8 + 364444960853480119379208T^7 + 145088936906457036995136T^6 - 946405361864597551050816T^5 + 1086632441482958356509720T^4 - 615454597853371985855184T^3 - 2089672621773109442565264T^2 + 1503858169634937349756032T - 268043453574349038086592,\nA6 = 22378678518203765279639595291703734T^12 - 97642937907003790975195419097186584T^11 - 57701568157490976356217548246274864T^10 + 692728062356311676289756774010506240T^9 - 165059119295086271477298303488050440T^8 - 2065127205357525454766777049159397680T^7 + 866901377553305534044230525750471600T^6 + 2900595200522009433908965902519647040T^5 - 1511852767062133534934112666639840240T^4 - 1121738997234616988726901721424515200T^3 + 1300199883149489416130125996732379520T^2 - 448873241175573293059242892011302400T + 53141649442568035635166156713288960.\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": "2026-10-23 07:34:32",
  "updated_at": "2026-10-23 07:34:32"
}