{
  "id": 5950,
  "curve_key": "525161159614759073554870225:-11757146861180192044480397886773394611225",
  "ainvs": [
    "1",
    "1",
    "1",
    "-10940857491974147365726463",
    "13607808867102145064563989807548302181"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 184.57724225411292,
  "faltings_height": 13.28413519050467,
  "conductor": "101702720970087871653296573403673618574885355370799850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "43",
    "47",
    "18077",
    "296982710898458736315429298113461470717"
  ],
  "discriminant": "3822871789261645562933636365158925449456612792301684307662253364126842880000",
  "regulator": "639898547841567.81572250626440105415967435791580428194167849149622371912400",
  "points": [
    [
      "5379488467131",
      "-10508477857710922622"
    ],
    [
      "338457690635",
      "3153341400683637202"
    ],
    [
      "-263800600389",
      "-4059021370732965182"
    ],
    [
      "1034808729579",
      "1842339660995408482"
    ],
    [
      "1614490413435",
      "-390124653362050238"
    ],
    [
      "817660234235",
      "2282227986062222402"
    ],
    [
      "56052727693455",
      "418942536372363223402"
    ],
    [
      "-2891268824215",
      "-4590357368625479038"
    ],
    [
      "2174476929755",
      "-314412396915675998"
    ],
    [
      "3523104705275",
      "4334942044074521282"
    ],
    [
      "1361975072379",
      "-1110435234494544062"
    ],
    [
      "3113120689275",
      "-3117447915221110718"
    ],
    [
      "2142329049595",
      "-35627169639721918"
    ],
    [
      "2527549577155",
      "-1449662246480994958"
    ],
    [
      "2636804393595",
      "-1758385893230153918"
    ],
    [
      "2307494897915",
      "805087706939885122"
    ],
    [
      "1567367807355",
      "556705951573317442"
    ],
    [
      "2510188074315",
      "1400357554393663762"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 25/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -17748181575995562432T^8 - 68950264390727535360T^7 + 8699074436586682108080T^6 + 12741479216727376275360T^5 - 463728474595265490031140T^4 + 2963699770894322471975520T^3 - 194193238987061701313153355T^2 - 95969453985039443759130870T - 310200641841234939840019575,\nA6 = 28458595086987432964730252544T^12 + 275888274364612261091053255680T^11 - 25546204540605639831811130845440T^10 - 214481134634159402629225293934080T^9 + 10021487135166118810532760404441760T^8 + 65631974027314075339317142302100224T^7 - 2153547550274428516604054291205834240T^6 - 8426270126123746622925669230499864000T^5 + 200045572563878379791949595562547381585T^4 + 160658159194208827721840972980051767780T^3 + 2225591631846316721268275361346593412191T^2 + 1041745904224145223737201675298702863910T + 2063542286683351976936829656813026126650.\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 07:09:52",
  "updated_at": "2026-10-26 07:09:52"
}