{
  "id": 6166,
  "curve_key": "424895463669645836086204154054112409:-295567223271061729898754394713871466013098790072812477",
  "ainvs": [
    "1",
    "1",
    "0",
    "-8851988826450954918462586542794008",
    "342091693600765887398192612490194091859453280864548"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 246.24147208717912,
  "faltings_height": 18.47003257210224,
  "conductor": "6367962895147526311451435040290000325942492681321729832833344746103158125918479216851612530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "59",
    "73",
    "5209",
    "1009927",
    "2392073",
    "1624406390313821083",
    "116122131419203006865591",
    "1083685101454426928930881"
  ],
  "discriminant": "-6163767456202031213404300398521772169572903269819683866487947358562336893472785944386225828883233519700",
  "regulator": "18513905380653232454953326.696138291228239518572308228992582379743884773171636364328077",
  "points": [
    [
      "9986474036124859",
      "-15958931194589233515668312"
    ],
    [
      "51679220911679696",
      "-4759166637482855084561854"
    ],
    [
      "948627888671543806/9",
      "650287239068189463887224606/27"
    ],
    [
      "48361278568748886",
      "-5206361123527890870482312"
    ],
    [
      "42486936389473834",
      "-6533962504157474098162922"
    ],
    [
      "90865548872231293",
      "-16970168975843222471223755"
    ],
    [
      "47927615122051584",
      "-5284828299739504853551162"
    ],
    [
      "140426900100186304",
      "-43222826088692450452962842"
    ],
    [
      "16333034894400593941/16",
      "65738271103975334098186403077/64"
    ],
    [
      "161672600035506874",
      "-56006882248499669783388032"
    ],
    [
      "31362088283411742064/961",
      "-279409704576842961869563356062/29791"
    ],
    [
      "526738191934898473/9",
      "133614643469425891592941838/27"
    ],
    [
      "136911927633407184",
      "41189148218124929334336238"
    ],
    [
      "28038907782295074",
      "-10767322500569317153547042"
    ],
    [
      "80196584467744093",
      "12164543858431456731349870"
    ],
    [
      "-121094173887769589/4",
      "-193051692846983846508797071/8"
    ],
    [
      "674814360609844327109/841",
      "17414699986065269763938819411302/24389"
    ],
    [
      "58777178572653106",
      "4985741473974648244794766"
    ],
    [
      "-92019359081306826",
      "-19428493533479233239600392"
    ],
    [
      "83881737972906574",
      "13775907860131209538148218"
    ],
    [
      "-34443750824005667",
      "-24619591581507033619976978"
    ],
    [
      "188785613489468383",
      "-73479822502515131428659980"
    ],
    [
      "175118904219736224",
      "-64515485512213563049906442"
    ],
    [
      "634906172464358540107/11881",
      "-6026757368966796140428888267664/1295029"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 9/166 of a rank-17 fibration of X1008 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -56986316681380998912T^8 + 24457666340476410624T^7 + 535487594425392365712T^6 + 48800690383254862104T^5 - 361470535143673852503T^4 - 1833035186758586060700T^3 - 8027564283553513223079T^2 - 1856193563269433892114T - 193818285257580953532,\nA6 = 176927718245814623549804322816T^12 - 116292625590383842700445954048T^11 - 3367104967138625608924904544000T^10 + 2020152346629037937923069338624T^9 + 29203681898463675958459856569392T^8 - 13720510267525899173180962213992T^7 - 142330533991632689827729911017922T^6 + 21328459230505455903018021874128T^5 + 318228745035755178053554583805228T^4 + 157407522251338495321687387801980T^3 + 99390588041592331039607736906018T^2 + 19564837728780267552757168309932T + 952356233459948553164561681844.\nIt is a 2-neighbour of the fibration given in curve#3589: 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": "2026-10-30 10:43:12",
  "updated_at": "2026-10-30 10:43:12"
}