{
  "id": 5557,
  "curve_key": "4803911737386146188149706826176:-11367652458146941112318162517988083020393224576",
  "ainvs": [
    "0",
    "1",
    "0",
    "-100081494528878045586452225545",
    "13157005159892259593573771066100641345083643"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 212.09420200623217,
  "faltings_height": 15.632150950833763,
  "conductor": "36685986496843233025077632858599740052959064837738121083639655160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "65633",
    "130911726458287877658056951519723689505792458201888741"
  ],
  "discriminant": "-10625533979687807938465211081786282964578901180986216571738885979200088552207289176800000",
  "regulator": "4769816002647405843.8290546658895424584512994116146431383154013410627401405148765",
  "points": [
    [
      "109570102706006",
      "1872570736187559430425"
    ],
    [
      "596018992005431",
      "-12854396489525635467150"
    ],
    [
      "-17726514039289",
      "3863357476034763705390"
    ],
    [
      "246700062919031",
      "1865820788155993700850"
    ],
    [
      "20908739638781",
      "-3327697106799608620350"
    ],
    [
      "220936113444131",
      "-1352734854635155896450"
    ],
    [
      "1595957993351",
      "3605174526114946176210"
    ],
    [
      "540570004325891",
      "-10817537499123867578430"
    ],
    [
      "-156382832332369",
      "4998359557793603915550"
    ],
    [
      "189324803777831",
      "-997612973556996028050"
    ],
    [
      "-311626007113609",
      "3752700455650929212430"
    ],
    [
      "32833037759131",
      "3147446577863192166450"
    ],
    [
      "-198174400703194",
      "-5020724417049257436975"
    ],
    [
      "18841868266751",
      "3358269195395159601090"
    ],
    [
      "210578486602751",
      "-1191528557628604969410"
    ],
    [
      "546920019253511",
      "11046084051126150862290"
    ],
    [
      "180084357590131",
      "986963480636312401950"
    ],
    [
      "174903316443941",
      "-1001457416496802140330"
    ],
    [
      "13968230481503369/64",
      "669583467253043203593915/512"
    ],
    [
      "-267111958972249",
      "-4564192354520788556910"
    ],
    [
      "51265102656671",
      "-2856754703548867596930"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -25/4 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4261577599459448669952T^8 - 64973986302543234990336T^7 - 520389045926789466560976T^6 + 1345632567339050301405168T^5 - 1166046837124054463831880T^4 + 1467990670474011670789248T^3 + 708396134646378930038064T^2 - 2039012801108036751604536T - 1064612557866595153534587,\nA6 = 114526854942132148192119773896704T^12 + 2886461604328553455092851655364608T^11 + 26297663143880669828973879786142464T^10 + 17285767061810088763243303592653440T^9 + 283423484340379516362999699927180240T^8 - 1873846284164641695090670451164046016T^7 + 1691887389529509979005107697145077168T^6 + 2214587379454712720775944886272688144T^5 - 1928086685736271044313072682680488360T^4 - 2342333230882985957665359245249370240T^3 + 626736207616137047035294839823032576T^2 + 1430459043024515641147100607262149672T + 441006788801640809301392680791854166.\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": "2026-10-23 03:04:29",
  "updated_at": "2026-10-23 03:04:29"
}