{
  "id": 6010,
  "curve_key": "499866785714464521257327328852840436816:-11289449913314432172317112031496557176829751826686863284160",
  "ainvs": [
    "0",
    "1",
    "0",
    "-10413891369051344192860986017767509100",
    "13066492955225037233006841802326122742228921126816922064"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 267.34243790855896,
  "faltings_height": 20.14382037067329,
  "conductor": "101298815660336815258920678759142994335374832436821638300165912738691271040045037122907378056",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "23",
    "37",
    "47",
    "67",
    "728590298213",
    "10343350349138373498601150036417708283754308390030731900138015826545993"
  ],
  "discriminant": "-1476599214515086734132199996584438996538127225721276031022080376691143978543899074047222307732312328383128064768",
  "regulator": "72560762634806271024868865.60835799864447570109173142111537959319545338105249237053960630",
  "points": [
    [
      "1594677472597646254",
      "717602819334212449989386838"
    ],
    [
      "2199773354854754096",
      "-896103594871890457588742196"
    ],
    [
      "20012186283824371582",
      "88426773161006174101931980134"
    ],
    [
      "1893915200219673746",
      "-369835412483121826836171054"
    ],
    [
      "-1275309403449515506",
      "-4926788546460193708983864522"
    ],
    [
      "1809488528181133100",
      "383916020891967513666120492"
    ],
    [
      "2441519723720151980",
      "1481457447218267731873612908"
    ],
    [
      "-1865959442841642814",
      "-5099165190651126745061239554"
    ],
    [
      "2310643003106364515",
      "-1157754283230906504168074892"
    ],
    [
      "1960187554042094366",
      "430128392614416988228321146"
    ],
    [
      "1707359461875034322",
      "513147297524978796307775214"
    ],
    [
      "5168502548058188519",
      "9864615599461605770608324878"
    ],
    [
      "5423342722103580806",
      "10775121908271273507980052654"
    ],
    [
      "-2119861576550953396",
      "-5061248798472481511053180188"
    ],
    [
      "-1742824700079106672",
      "-5091400416262145189298944580"
    ],
    [
      "6211397778723272150",
      "13712274824943258955989768258"
    ],
    [
      "2555448088240062734",
      "-1772629395230515618890622518"
    ],
    [
      "17190183782976406114/9",
      "-10240166875286966028269161958/27"
    ],
    [
      "1870920800849881106",
      "363035229566902303335755346"
    ],
    [
      "-1597253763344564087890/961",
      "151271674546792333693814118780822/29791"
    ],
    [
      "2840261385920511062",
      "-2530009625970906442605356994"
    ],
    [
      "2094123947223609206",
      "664823887029969199444301346"
    ],
    [
      "-31951598819778137345/9",
      "62112122971060043051669136734/27"
    ],
    [
      "1629091257976477772",
      "-651783163184244294235140636"
    ],
    [
      "2820581157815092202",
      "2476469833429387203585569226"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 271/34 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -80918153007142747807152T^8 + 354290935210738441284960T^7 + 117546745373133609199680T^6 - 1321723369189316995545600T^5 - 1222018032904985784972240T^4 - 1406850947577826580594160T^3 - 1254988108939355569153800T^2 + 805670525674002972117960T - 100416874821843548929275,\nA6 = 8831810495179731787950781376781696T^12 - 58200269129275243642314244480725120T^11 + 52846203831582430953753256517509440T^10 + 303184046482963991294863102867915200T^9 - 457715356448899454589683173529277360T^8 - 744423311865278126846298019797769248T^7 + 1833256433177951161172716555006515840T^6 + 2794775310889560685872413753874966720T^5 - 133387102323757291083447813526175040T^4 - 778071888245494603901822019677467920T^3 + 439063195335888681561403448200034856T^2 - 128557299724393005377297960904774360T + 14412007642333428007694069449224150.\nIt is a 2-neighbour of the fibration given in curve#4205 (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": "2026-10-28 00:47:56",
  "updated_at": "2026-10-28 00:47:56"
}