{
  "id": 4608,
  "curve_key": "834817902412981693093294217224604961:-789204787743968455320580498268038036534921831925884209",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-17392039633603785272776962858845937",
    "913431467296259790598681781396360712331881723884961"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 248.20573116681032,
  "faltings_height": 18.603540347476287,
  "conductor": "10258814917561359743040473223746249383896581362469061792611616516072656890",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "167",
    "2539",
    "131591",
    "85256873355920076737297402339577182685267751731301363"
  ],
  "discriminant": "-23751231429248518048769053899687622491790635613026186809384497877981425273238270692927098072958976000000",
  "regulator": "213466848627958616658.6025584842471602631937550697399896368366783539756445729624609",
  "points": [
    [
      "-102144673279320569",
      "-40301435695312980551427116"
    ],
    [
      "-127780951948521769",
      "-32394429754126736260628716"
    ],
    [
      "178814464393046871",
      "-59338069280910418599516396"
    ],
    [
      "60033084062719871",
      "-9256953896353571096032396"
    ],
    [
      "64261330401243351",
      "-7820755765081802336373996"
    ],
    [
      "148610896593602931",
      "-40135844741147137805579116"
    ],
    [
      "452392851507324831",
      "292629112820022919897092084"
    ],
    [
      "70780978395535511",
      "-6083981397429245176290476"
    ],
    [
      "28786475679849991",
      "-20895697569749772513928236"
    ],
    [
      "16957484969833511",
      "24967627996411724611002964"
    ],
    [
      "76105889146375191",
      "-5532470704952123741312556"
    ],
    [
      "66677924433965591",
      "-7086098258982298101874156"
    ],
    [
      "102604780328954391",
      "-14461037648188773980245036"
    ],
    [
      "-7430079495110169",
      "-32283827507646480479577916"
    ],
    [
      "141682478285779919",
      "-35963976260220376189536844"
    ],
    [
      "71555340291363031",
      "-5942510048594291931022316"
    ],
    [
      "25126203285879799",
      "22187797796650717038495636"
    ],
    [
      "70007413694822581",
      "-6242495251366420107789416"
    ],
    [
      "687136370854856311",
      "-559820112746345990675732076"
    ],
    [
      "47387628705545231",
      "-13988459927485690855672516"
    ],
    [
      "-150439318405840361",
      "-11186470681110855932265516"
    ],
    [
      "38933644107196711",
      "-17184665242725156717672876"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 175/4 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -951794051889111932592T^8 + 44931125401781237315136T^7 - 935996917001646313472256T^6 + 350884544094515993044032T^5 - 1398456319949084806406280T^4 + 1757156899789831824711432T^3 + 1161615213018494249920164T^2 - 1209850628288081766896304T - 608061871140582830645232,\nA6 = 16573004223094294578838161979776T^12 - 853911819873454385971944861242112T^11 + 10730626760581365984133349196446976T^10 + 28681501792522102389650863794343680T^9 + 1144251410928840595115561345197638240T^8 - 1598280314283758871148427065729397664T^7 - 426571032276915684981278470103405232T^6 + 1752000471251825933878865739300711456T^5 + 357646791216195149324748670252742580T^4 - 1462595841433547195589341024424494400T^3 - 249356805352454598151173826415660496T^2 + 545782915696199470675908824491330752T + 182530075488483105810112141784098944.\nIt is a 2-neighbour of another fibration built here: 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": "2026-10-19 01:37:46",
  "updated_at": "2026-10-19 01:37:46"
}