{
  "id": 5572,
  "curve_key": "2250879543555065039718945477601:-3447330142239940028112782160175834436356376401",
  "ainvs": [
    "1",
    "0",
    "0",
    "-46893323824063854994144697450",
    "3989965442407334087723919939326707011502500"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 209.7078584887349,
  "faltings_height": 15.372395240838319,
  "conductor": "8776494935164573743061478341642752334670942606930849619330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "43",
    "61",
    "20660855002775102359",
    "277103508797052601070452468783"
  ],
  "discriminant": "-277833807519816109730640926576027610664556420015317962482438289970800574775937024000000",
  "regulator": "18137288568035440.09006007687430233768408068257110214182629858009742519600254",
  "points": [
    [
      "94061978614900",
      "641338110502808724550"
    ],
    [
      "146364036243700",
      "-511803529007555387450"
    ],
    [
      "100431415534900",
      "541664914288241364550"
    ],
    [
      "1927403965460500",
      "84105252639060507552550"
    ],
    [
      "64516105088500",
      "1110462940290464858950"
    ],
    [
      "339256588389700",
      "-5208439911080073952250"
    ],
    [
      "842440733233780",
      "-23714356623230452389050"
    ],
    [
      "-226402216882700",
      "-1732570599304477249850"
    ],
    [
      "190884730486900",
      "1412093787147579156550"
    ],
    [
      "126612669716500",
      "287010166571630052550"
    ],
    [
      "489806330068120",
      "9926271626906104047430"
    ],
    [
      "1135985550250000",
      "37638641036785157197450"
    ],
    [
      "51045451781620",
      "1315021084075644831430"
    ],
    [
      "107614071138100",
      "-435706070747713067450"
    ],
    [
      "-249629175887180",
      "374611473378743132230"
    ],
    [
      "413162543782900",
      "7425873817101676788550"
    ],
    [
      "78957834022132",
      "-882961030044772965434"
    ],
    [
      "138721838450260",
      "392893702483746971590"
    ],
    [
      "-17194193753210",
      "-2188875282823382445440"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1/15 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -213546515196627504820332T^8 + 869465515207593907398960T^7 - 510065089965030971860884T^6 - 1270257582515056045578720T^5 + 1426065508735989008931900T^4 - 690890144029437273227280T^3 - 1389292332816820391566956T^2 + 1307996517837724132656960T - 286267614586960854758400,\nA6 = 38855172470975738993518813988244756T^12 - 243637332934783116837818686074203520T^11 + 382613702852074064448992630465758608T^10 + 438404888400781537256687728554749760T^9 - 1340270054837389026155362835012033304T^8 - 438466811942831565597983911599431040T^7 + 1981768199902501016022471226901183040T^6 + 697917175039489822346233336938891840T^5 - 1626320407404938608434545478196300764T^4 - 187748176254897658526766053163492480T^3 + 919892555571017546557734659258394000T^2 - 417938005135807422838969764298752000T + 59851413200989840657350337781760000.\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 15:10:46",
  "updated_at": "2026-10-23 15:10:46"
}