{
  "id": 5949,
  "curve_key": "477715933307885333055448896:-10420338294665388191008880673145694722944",
  "ainvs": [
    "0",
    "0",
    "0",
    "-9952415277247611105321852",
    "12060576729936791887741760038363072596"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 184.2931755177314,
  "faltings_height": 13.157303253504718,
  "conductor": "36045808353412385345967267638753921112218444223303632141850120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "92111",
    "91914671",
    "6005710770739",
    "27354875528749",
    "541259007961240039"
  ],
  "discriminant": "253069117243117787532333072413255298078895324560822523941107430076692000000",
  "regulator": "1229179894514986363.96098253057209710331914692525635687914237114032305115536849",
  "points": [
    [
      "1696975404372",
      "-241653003909719850"
    ],
    [
      "3194513372382",
      "3587086932773467410"
    ],
    [
      "6922321435713/4",
      "-1132839101492820225/8"
    ],
    [
      "1922040707772",
      "-179192683326154050"
    ],
    [
      "1542834781722",
      "-614910019511450250"
    ],
    [
      "5154431161722",
      "9884598737509077750"
    ],
    [
      "2027794791102",
      "466170720258008430"
    ],
    [
      "1897912430802",
      "90446202354533130"
    ],
    [
      "-3629519098818",
      "-608209585632600210"
    ],
    [
      "229311997956012/121",
      "101867615075181504150/1331"
    ],
    [
      "1459106546922",
      "803348295033775050"
    ],
    [
      "1576769088681",
      "536731281121242375"
    ],
    [
      "658713257142",
      "-2406367928400421230"
    ],
    [
      "1888683791956",
      "-28022226362755030"
    ],
    [
      "1727722411537",
      "151195019161117085"
    ],
    [
      "1299572179257",
      "1149576609794855535"
    ],
    [
      "1941172820772",
      "236331937226564550"
    ],
    [
      "1598807675922",
      "-485209814360791050"
    ],
    [
      "2490083059222",
      "1648644906492032750"
    ],
    [
      "2279009346022",
      "-1102650698295386450"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -13/10 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -10669947921935414766592T^8 + 11909462495223346810112T^7 + 29290850738695015599056T^6 + 749826724411797003953776T^5 - 2800296645908250177432680T^4 + 5291011042236720751525024T^3 - 9053743075112346775820704T^2 - 1373686135035664689321352T - 153062929487822447776267,\nA6 = 424084459520579325699737587892224T^12 - 702971076900016054991835746922496T^11 - 1428460164091780099364248773693184T^10 - 45531551300070380060674898437602560T^9 + 178145138683306119166957105019549520T^8 - 224307849011465835658368095576866752T^7 + 1890363249575504635685922631864051728T^6 - 8402714629932209203714457518206796848T^5 + 10932033646871752694840038266436614840T^4 - 1045636958253350245306227479236779680T^3 + 3911537622199302231442442603656239344T^2 + 397823992391227625022128206594583384T + 16543056563137220502197778370669126.\nIt is a 2-neighbour of the fibration given in curve#4205 (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 06:42:38",
  "updated_at": "2026-10-26 06:42:38"
}