{
  "id": 5869,
  "curve_key": "10057081207168898769704656:-32762703352986553896162223625961023680",
  "ainvs": [
    "0",
    "1",
    "0",
    "-209522525149352057702180",
    "37919795547368300241804641473776384"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 172.76470824659674,
  "faltings_height": 12.305848914647592,
  "conductor": "422671728388089957192729904126853989535909583389370024",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "23",
    "41",
    "73",
    "1224083711877913792680140539558133360616296401"
  ],
  "discriminant": "-32507196141849826359147109990099089797351128372627336751068152004009728",
  "regulator": "2167392724958702.6218458860014548376049793848327892151839130118906723631573",
  "points": [
    [
      "245080808218",
      "-35923906856848230"
    ],
    [
      "-526531210640",
      "-47613057330528072"
    ],
    [
      "286831056394",
      "-37688310424662678"
    ],
    [
      "8366855675506/25",
      "-9086226188175809046/125"
    ],
    [
      "-6935029532",
      "198425066232033720"
    ],
    [
      "-233540306261",
      "272239253161938648"
    ],
    [
      "-416208480668",
      "230272144780611096"
    ],
    [
      "2146526815339",
      "-3078711167541259248"
    ],
    [
      "-73661803586",
      "-230117164026254802"
    ],
    [
      "621354903106",
      "384221080241945166"
    ],
    [
      "-918731393",
      "195223691424203046"
    ],
    [
      "460917507394",
      "-198158501433273678"
    ],
    [
      "10105760885782/49",
      "20234889598129930170/343"
    ],
    [
      "172020662884",
      "83473792142654232"
    ],
    [
      "677415267487",
      "454803373818859986"
    ],
    [
      "362037305472",
      "-97557268273527984"
    ],
    [
      "-411943114466",
      "233078512615653582"
    ],
    [
      "-412882353782",
      "-232471794306126870"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 2/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -1514324488040382021552T^8 + 54272277189707511223872T^7 - 591511378048151427927072T^6 + 508063749731038184428512T^5 - 136938741575533789662000T^4 - 1349191793967592327593264T^3 + 2932284504423022894260000T^2 + 1053383284052353089252396T - 2783171113600789327601367,\nA6 = 44549962755947395534698409178496T^12 - 1693056117252550785873714686294784T^11 + 21575677941893867020743091398042240T^10 - 126989060702986786740910506616083840T^9 + 604500920208636167244898036604209536T^8 + 157197955421771732041959401485834176T^7 - 2431613790180256867483636634863226688T^6 + 80227062221723361472990833995217840T^5 + 4121456489545992568565603195410675236T^4 + 44671471294135497947381190393251640T^3 - 3860959108216677291627323697767945196T^2 - 282581272382058990631068152666505732T + 1744104189782696812246440603003980826.\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": "2026-10-25 17:34:01",
  "updated_at": "2026-10-25 17:34:01"
}