{
  "id": 5940,
  "curve_key": "329717001942921915622991935271467881:-191752515743845311584138818818023532229315661268055221",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-6869104207144206575478998651488914",
    "221935782110932075310029314306912213579605752302848"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 245.37609060554675,
  "faltings_height": 18.323303395119062,
  "conductor": "4724989468798958486439099758364047973605979150400585210554533569409780360104561775212290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "47",
    "232366635961",
    "4704013299320244929",
    "7146314557069327440124910917308024206632464207787469"
  ],
  "discriminant": "-534955726264159471005775930405193349007818809439620591349995668149634040334395060166899590205310937500",
  "regulator": "6086406330887864905172000.8294492650507124739559551338840866283050156228103956510755877",
  "points": [
    [
      "44284155896547637",
      "-2142045588190986218694131"
    ],
    [
      "54707718364695037",
      "-3143147912932972150934906"
    ],
    [
      "73166265667487062",
      "-10537088188031022201161756"
    ],
    [
      "46528771101969512",
      "-1748192296858834304484756"
    ],
    [
      "48153277341361262",
      "1679506406405193043063494"
    ],
    [
      "178542819510616423/4",
      "-16508419769382525069209173/8"
    ],
    [
      "56646203422510387",
      "3820080173912988170376244"
    ],
    [
      "-43516802888410496",
      "-20939172317822339975627840"
    ],
    [
      "59942707812696637",
      "5056175472049960382327494"
    ],
    [
      "9191890695036262",
      "-12632195291472963896267756"
    ],
    [
      "13552330718996282",
      "-11460039623889286617057906"
    ],
    [
      "14174602165129762",
      "-11287910112519659414302256"
    ],
    [
      "1495755650634426262",
      "-1826575776599767874524776506"
    ],
    [
      "38550516182799262",
      "3797344041979216968911494"
    ],
    [
      "53737899895570642",
      "2826093914167535672205664"
    ],
    [
      "48916652778792154",
      "1723910434057416523284760"
    ],
    [
      "51715524424327912",
      "-2238166984058463883637156"
    ],
    [
      "-69490480589856113",
      "19071147986205683429608369"
    ],
    [
      "-80496141933604613",
      "-15914994286977337189358756"
    ],
    [
      "51272870641691912",
      "2128077214874640984833844"
    ],
    [
      "103668092966628832",
      "24979140510158241772652824"
    ],
    [
      "59286265252052662",
      "4803669847421074502375494"
    ],
    [
      "35286971024933137",
      "4846048902283146915590869"
    ],
    [
      "56286779553464827",
      "-3691055465299587202732631"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 19/33 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -6195147929170777488267T^8 - 76325725939813122988800T^7 - 882325168895840084876340T^6 + 137101400449928233205328T^5 - 540371179907883674625330T^4 + 1432666851749665397357472T^3 + 819022076707710173673708T^2 - 1550804727906185486991696T - 817873967341793893325067,\nA6 = 184510578295520929147533147781830T^12 + 3583110577624752524437698479790336T^11 + 53501492723177054560052620493555580T^10 + 169407308640762620085933160597599120T^9 + 698545865865095496350873237321288874T^8 - 1292699670982664072004165953289975552T^7 - 505316963797428638034138121593355512T^6 + 1943998258237962328932351927104831040T^5 + 142849376365152697481163983826326634T^4 - 1559076824193899778858619351522756800T^3 - 52912284260963932942946689331970468T^2 + 820349089697858180287004856848627568T + 284805687406045189533586630147368774.\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 23:37:42",
  "updated_at": "2026-10-25 23:37:42"
}