{
  "id": 5607,
  "curve_key": "8943805168713931059252302881:-844985223348082260966607367144554135967665",
  "ainvs": [
    "1",
    "0",
    "0",
    "-186329274348206897067756310",
    "977992156652857459790340620657367196196"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 193.0822759306575,
  "faltings_height": 13.863606618122533,
  "conductor": "693682949767109880007607327128963298701962287032571394",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "23",
    "31",
    "1212719",
    "3656069",
    "3319150932761",
    "4532457222976163741023"
  ],
  "discriminant": "827380243187373935520640603532643612499327835652428650049853408325101479657472",
  "regulator": "5408244993348377.5707173765820920620187527589431717346295852110435059419477",
  "points": [
    [
      "15205277009132",
      "40746413047642338074"
    ],
    [
      "21909649177340",
      "-86098395190831566934"
    ],
    [
      "202266075063596/25",
      "33049148645417071666/125"
    ],
    [
      "255121795346732",
      "-4069224489809953155046"
    ],
    [
      "11135226896666",
      "-16848349519879951672"
    ],
    [
      "7553331202328",
      "-1234597546083534322"
    ],
    [
      "256702455398504/25",
      "-1517347738289542845902/125"
    ],
    [
      "7344904501196",
      "-2379407675980683622"
    ],
    [
      "8328658214996",
      "-1962039380960330374"
    ],
    [
      "-15683430730420",
      "6528482043318712346"
    ],
    [
      "2986960820300",
      "-21167981666677782886"
    ],
    [
      "7676461098854",
      "-40653522468226084"
    ],
    [
      "-10306536633820",
      "42468733809402058274"
    ],
    [
      "189470252448956/25",
      "134187617820587944306/125"
    ],
    [
      "24264811988080172/2809",
      "537063399441452529715666/148877"
    ],
    [
      "5920242887756",
      "9076219904279223578"
    ],
    [
      "-2186137467460",
      "37079450696667391466"
    ],
    [
      "982329939625868",
      "30785368371406767420314"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -3/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -15108348426986418946992T^8 - 165645727401183163968960T^7 - 386516497356749936802240T^6 + 804907699137855510269760T^5 - 423101056239642087896040T^4 + 2012740403434408357952040T^3 - 832891923170874739577340T^2 - 2371900038780270082074480T - 881248331824987560372900,\nA6 = 717503217218577271350459150984576T^12 + 11638864686052244686069138775512320T^11 + 58135061140664436934300824832212480T^10 + 62512031622436328327919258342862080T^9 - 268895690113423321891997914072476960T^8 - 870815838806588886732350721838471968T^7 + 2170770437820474859902147687346459920T^6 + 114853264658855014380401497670938080T^5 - 2228934495975748087928517866419014780T^4 - 844990471869666800949969469071688800T^3 + 1481780271644919349838123819347167336T^2 + 1307631772289943212553000319429645920T + 318018311456252316549507444881168100.\nIt is a 2-neighbour of the fibration given in curve#4647: 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 22:31:56",
  "updated_at": "2026-10-23 22:31:56"
}