{
  "id": 5948,
  "curve_key": "50055913719342507339424425:-362021151321207552250667241195148783125",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-1042831535819635569571342",
    "419005962177584263729634586201592816"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 177.56953197393722,
  "faltings_height": 12.697116771500811,
  "conductor": "2650707450869817434112548686478311491876599015417068299650",
  "bad_primes": [
    "2",
    "5",
    "11",
    "17",
    "19",
    "23",
    "61",
    "71",
    "49480609117",
    "3027230776506670314004689318653554561"
  ],
  "discriminant": "-3263594897255048104065265859787547184329099909073499493802787495705687500",
  "regulator": "30567620285552021.59616668724788261525958243328138220261219918212692749864332",
  "points": [
    [
      "640839261979",
      "-117878259312442752"
    ],
    [
      "556494095634",
      "-104950844357077292"
    ],
    [
      "544267120269",
      "-112488036936828247"
    ],
    [
      "432842516959",
      "-220722498141761292"
    ],
    [
      "616724196334",
      "102160294866488208"
    ],
    [
      "506048107393",
      "-144479346088772191"
    ],
    [
      "540825319654",
      "-114906132469506952"
    ],
    [
      "361185262567/4",
      "-4564758165833905481/8"
    ],
    [
      "7509234349081/9",
      "9725747562758778266/27"
    ],
    [
      "-963821145602",
      "-727162661561528832"
    ],
    [
      "-1029473016216",
      "-633657328320833192"
    ],
    [
      "491241079572466/729",
      "2937546289468261218284/19683"
    ],
    [
      "681208412329",
      "157262616297420998"
    ],
    [
      "601406054759",
      "96761587162014333"
    ],
    [
      "16549800389819",
      "-67201814113727193947"
    ],
    [
      "42658351512637/9",
      "272633435884207455718/27"
    ],
    [
      "589402834354",
      "95467553857540148"
    ],
    [
      "441895767713",
      "210885844870990078"
    ],
    [
      "2356466530829",
      "3323688439282677673"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -51049289999914003955547T^8 - 530235497365547560296156T^7 - 1334884185331356871311696T^6 + 296356690966601689934112T^5 - 953952652223826315944400T^4 + 1047754795078929750243552T^3 + 682302168670760680583648T^2 - 366523380774730949131328T - 202247154940524926594992,\nA6 = 3044477113558101150415568243130870T^12 + 47916509824848437926710847832831508T^11 + 305385110180964852636417452183552148T^10 + 946395756942760565659602913027215240T^9 + 758039466954512559172972729736599956T^8 - 2347628404098854859298591084323198768T^7 - 233574834077417409656982537875304960T^6 + 1478394126214621260825428576579913984T^5 + 245358536538278262563954912437168896T^4 - 564843727808435860192153910652566400T^3 - 138927685606375319261165262679233920T^2 + 99890538814857739577414321265656576T + 35404124129085042130410014629000576.\nIt is a 2-neighbour of the fibration given in curve#4647: 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": "2026-10-26 06:09:47",
  "updated_at": "2026-10-26 06:09:47"
}