{
  "id": 5955,
  "curve_key": "1803323130033417178263199201:-75252069102392617010947984428060249409105",
  "ainvs": [
    "1",
    "0",
    "0",
    "-37569231875696191213816650",
    "87097302201840175956311266553579692836"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 188.2782859709741,
  "faltings_height": 13.579443910949877,
  "conductor": "332357300745286461617008299428048474894422214129747622",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "29",
    "31",
    "59",
    "83",
    "93339548881",
    "5937695664415267",
    "249481963259350747"
  ],
  "discriminant": "116601035691487875177470953655526486544438111627034485987860597910955111841792",
  "regulator": "1013769155564367.2372121125159314609990383507809012683485732030084114155672",
  "points": [
    [
      "1392618625764",
      "-6121970647975165530"
    ],
    [
      "9985811622516",
      "-26602402499310103194"
    ],
    [
      "5807020304724",
      "-8046949959315894810"
    ],
    [
      "2780618208468",
      "-2032463061467723802"
    ],
    [
      "16419516881784",
      "62425460910609959910"
    ],
    [
      "6944033020836",
      "12690692829007872678"
    ],
    [
      "3149023578612",
      "133128361842039654"
    ],
    [
      "2474862224928",
      "-3045821250790823142"
    ],
    [
      "4806005561268",
      "4188910206202720998"
    ],
    [
      "7597392276084",
      "15498170247243650406"
    ],
    [
      "2694830338404",
      "2329108394774691750"
    ],
    [
      "405670542584946",
      "8169790198872998256378"
    ],
    [
      "3952550427828",
      "-593592682084825242"
    ],
    [
      "-291723093660",
      "-9901125468245506314"
    ],
    [
      "2714301962556",
      "2262852164424418566"
    ],
    [
      "6756970558704",
      "11905615295365187850"
    ],
    [
      "1547846596788",
      "5714390742082156518"
    ],
    [
      "216832521167628",
      "3191647254487203872814"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 13/15 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -12534891445024511472T^8 + 78582946111770655584T^7 + 7309714285353743792064T^6 - 19926705130047311795712T^5 - 1581992160157740826540080T^4 - 21656860033375553017441392T^3 - 202996255697903740935519336T^2 + 178453288354749583292951064T - 417819161395360164489662107,\nA6 = 17317363417405211174636142720T^12 - 210396669596964946038298988160T^11 - 14361293747299826509324376137920T^10 + 234213338250246103165559236334400T^9 + 4592862633125351988053413995183120T^8 - 107548397787843527128824559544935200T^7 - 702154954133939094763560787985051520T^6 + 29466052944788501707392754934785197120T^5 + 255347880900757963651505245178114673120T^4 - 1780579839791453417816567234531995600T^3 + 2459557153650501225624269205923573478216T^2 - 2269524913223376034392201865605330615368T + 3342509745342723924186855161219248634806.\nIt is a 2-neighbour of the fibration given in curve#4191 (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": "2026-10-26 10:58:56",
  "updated_at": "2026-10-26 10:58:56"
}