{
  "id": 5957,
  "curve_key": "6446334982497702633236161:-16215705807755858215334560192485093409",
  "ainvs": [
    "1",
    "0",
    "0",
    "-134298645468702138192420",
    "18768178018224755454700015785341712"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 171.37666194419685,
  "faltings_height": 12.14316256163129,
  "conductor": "206949144765162170184985203856017325963636347448295010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "71",
    "155607247",
    "339003367",
    "6373123858691379307668994949857"
  ],
  "discriminant": "2852921499537815021766522110132607550935999640924770304016034816000000",
  "regulator": "2543200479609859.6718812392158245389983449069906438436089709545412899525818",
  "points": [
    [
      "146078373864",
      "-47615205284716932"
    ],
    [
      "192967064964",
      "-6192011376770832"
    ],
    [
      "127508728164",
      "60967354643945868"
    ],
    [
      "124781867064",
      "62873303543818668"
    ],
    [
      "233818704164",
      "12238703576364368"
    ],
    [
      "74026608264",
      "-96084198442149732"
    ],
    [
      "180749448864",
      "19972941965248068"
    ],
    [
      "-422602185336",
      "-7032075418154532"
    ],
    [
      "324634229064",
      "96863620964186268"
    ],
    [
      "320344430364",
      "92845291372748568"
    ],
    [
      "194271276744",
      "-3140935020426852"
    ],
    [
      "-334331688888",
      "162165672259746588"
    ],
    [
      "526186910424",
      "-306249770366790372"
    ],
    [
      "346220289144",
      "117354694449565548"
    ],
    [
      "234303144264",
      "-12819967214901732"
    ],
    [
      "-345504624336",
      "154676944273293468"
    ],
    [
      "341524021464",
      "-112857903409519332"
    ],
    [
      "194379225144",
      "-2756304665476692"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 61/12 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -159593418515992752T^8 + 66594122607180400704T^7 - 9577916877180584429856T^6 + 378921666915696440595168T^5 - 8319401481873790592668080T^4 + 116272680309493432400708928T^3 - 728840755857976029224439616T^2 - 494050735965340585862790156T - 1390993922871848594371288527,\nA6 = 40790046358717726655041920T^12 - 19761746514541051225237666560T^11 + 3565895854811577447633633290880T^10 - 339557681946125505951450862243200T^9 + 23467317247680868700633154198453120T^8 - 886973909798626440691615033339785600T^7 + 17462193623232977878169289412672255680T^6 - 168744348646923648755279986373234058480T^5 + 648041970284178877886227382317646179620T^4 - 1598469487562293877807341226375296120200T^3 + 21038628236849997090209222042624669117476T^2 + 9643147208228838672635695562458112132532T + 18608807243853177902952156937051966196946.\nIt is a 2-neighbour of the fibration given 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": "2026-10-26 19:33:58",
  "updated_at": "2026-10-26 19:33:58"
}