{
  "id": 4598,
  "curve_key": "87694229223150605245114154519632:-843410124041425251838025767848291122552479749056",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-1826963108815637609273211552492",
    "976169125047946502318751280962873371802554244"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 220.70756505963152,
  "faltings_height": 16.30073458593938,
  "conductor": "173039907622860632316198002562592374305691525164830978998135893514401376916587672",
  "bad_primes": [
    "2",
    "3",
    "19",
    "23",
    "41",
    "199",
    "7545367",
    "10109588809",
    "735626069114435882576923",
    "36036756176284798194279666008839"
  ],
  "discriminant": "-21381741741241697137655837913627601564078594269615265565791393167893992282630997786086361856",
  "regulator": "186819834376899502576183.567343835547414873072116047491716916752316808009068214167698",
  "points": [
    [
      "971218727898604",
      "-10858442146651919301318"
    ],
    [
      "-1482395970896498",
      "20661315791096183094708"
    ],
    [
      "3509108905670874",
      "194359926055932437058228"
    ],
    [
      "165490103006222",
      "-26045289116493005398028"
    ],
    [
      "-298110552101916",
      "-38656345543165643134242"
    ],
    [
      "328840085382824217",
      "-188570375402345999327354052"
    ],
    [
      "-946802274467076",
      "-43095193280598440302122"
    ],
    [
      "4578010360988600",
      "297588765037641409634138"
    ],
    [
      "3381648858960960",
      "-182945436286787722216482"
    ],
    [
      "789257506929424",
      "-5086738927656671404878"
    ],
    [
      "-1552806959920252",
      "-8303453060716028510846"
    ],
    [
      "2950337811756248/49",
      "-10096000812815021995060106/343"
    ],
    [
      "1114491952055069",
      "18009312260835870022862"
    ],
    [
      "741905074879812",
      "5394223205888881131582"
    ],
    [
      "857109297867068",
      "6318678854316166814186"
    ],
    [
      "-911059123789795",
      "43410082807843225540978"
    ],
    [
      "1100495045254464",
      "-17274348006770675188002"
    ],
    [
      "-592761927980422",
      "-43021465518090717238844"
    ],
    [
      "-1368398042920712",
      "30229761231636446441574"
    ],
    [
      "818438235123130",
      "-5397802045677115854372"
    ],
    [
      "3848249991849960",
      "-225686508759099486483018"
    ],
    [
      "9461743920489322/9",
      "398119691888505537132068/27"
    ],
    [
      "721259672949614",
      "-5802136115143968613052"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1174/561 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2543951687432473887460672377483T^8 - 24818956579468052738105064515028T^7 - 77370351271537068433100341247904T^6 - 67467015005869076752518330881556T^5 + 17016806163007175905444072313970T^4 + 82892666432004286839667115406660T^3 + 60326950313063858115906668276136T^2 - 19915299958127111246160446427612T - 27289787224140550157486254128927,\nA6 = 1550015425870788606577153334191333100109899718T^12 + 22628758087381124339269406905403241577644202332T^11 + 129666144682594016426381124339897213302125685892T^10 + 345383914891725536644308394433318665228830332532T^9 + 290839421645428584216690391576246831863346739238T^8 - 501824346857271485681078887124327532393736266360T^7 - 846300710982340207425925322969763595750992960552T^6 + 305997138248518386594529888488269900783383863000T^5 + 830499992755676217073833197525717220681011885394T^4 - 107750490807943398511372493107734289465806190692T^3 - 406158893855534218232938145420042389062774860796T^2 + 16099138820538211319454876432431072682872064564T + 80603603306668130852282428774716725293282315746.\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": "2026-10-18 21:24:19",
  "updated_at": "2026-10-18 21:24:19"
}