{
  "id": 5978,
  "curve_key": "459895262824063291833373451736241216:-309795023165139573889937306673251796554909572358366080",
  "ainvs": [
    "0",
    "1",
    "0",
    "-9581151308834651913195280244505025",
    "358559054589281911030747372371379682354940812431619"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 246.34892052854565,
  "faltings_height": 18.37703569014648,
  "conductor": "8695817217975270702029545916305160192036786620186268139060193767787379278516836054936696",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "19",
    "4297",
    "4433494036989996753503482173009288536566211848419182927816620424488210611555703"
  ],
  "discriminant": "750330787098362628719549912478826355733233216408508001633786954797313945286282955279611630172051148032",
  "regulator": "8781930743394985947625472.7583067436271862537678471742624121300392099296528429242424972",
  "points": [
    [
      "51879414612319043",
      "-1061419486809136817191830"
    ],
    [
      "51387341553492239",
      "-1380434418907215642519822"
    ],
    [
      "52677348210729950",
      "154735841653322592922287"
    ],
    [
      "99388176831748127",
      "-19699321517808771211381134"
    ],
    [
      "96063831472556081",
      "-18018294486471877166690814"
    ],
    [
      "60723399427049927",
      "-816250130433002031682734"
    ],
    [
      "178694600410338041",
      "65973420270204672315307014"
    ],
    [
      "104347325649227055431/1681",
      "119417476071069018829195312194/68921"
    ],
    [
      "-35205664336150405",
      "25538883787598566754130762"
    ],
    [
      "-7046394180992599",
      "-20633025909298367382822186"
    ],
    [
      "95176235664076043",
      "17573177788398908974550070"
    ],
    [
      "747410914376080390/9",
      "-314427912434661591189497951/27"
    ],
    [
      "41925178978669307",
      "5528139221498752826559306"
    ],
    [
      "-165367927691230267/4",
      "-209227577366361463273266903/8"
    ],
    [
      "1570021289682156137",
      "-1963508691212624255716293354"
    ],
    [
      "487364643496384319",
      "333841262238552151260704142"
    ],
    [
      "112805617320696161",
      "26706084529571955607187214"
    ],
    [
      "60306248852337107",
      "283121350912736675314794"
    ],
    [
      "2399849300941141001/64",
      "-3692541828762973677838998651/512"
    ],
    [
      "72167101894572665",
      "-6554993251331805328957062"
    ],
    [
      "2464116183377350121",
      "-3865040631592981113128888214"
    ],
    [
      "62228162686923059",
      "1819472183301659731419498"
    ],
    [
      "-23291223786847423",
      "23855413327605854443359534"
    ],
    [
      "52692052111885793",
      "-74180511366558213744270"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 113/64 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -299179532755056721600T^8 + 17595572277256973050240T^7 - 417198241841028433831120T^6 + 1640729978369826838604080T^5 - 3100722994060599052732840T^4 + 3447605855872936235820160T^3 + 2242797006715822622440160T^2 - 6780974649680701579123160T - 3861433387934633535827467,\nA6 = 4059456937701100750406882080000T^12 - 282164040891383692833079679552000T^11 + 6335982179671782376102889433278336T^10 - 57358833600342341658935952553773440T^9 + 596470207133623029963843326957746320T^8 - 2651283194034110828378464332085379520T^7 + 3864693449523759808880763001015666800T^6 + 2106280696838105770175445350531933136T^5 - 6473880048439824158203228245177202440T^4 - 4211251865396149188236650636780633280T^3 + 4195370517911125633418237460366830320T^2 + 7286118774738610034794421910368398280T + 2836757717663966250804688091791547974.\nIt is a 2-neighbour of the fibration given in curve#4187 (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": "2026-10-27 14:51:29",
  "updated_at": "2026-10-27 14:51:29"
}