{
  "id": 5865,
  "curve_key": "538629671849065856656279603921:-387076573923412704804641290349663828468770969",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11221451496855538680339158415",
    "448005293892837843588117496239443106538617"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 205.376477341187,
  "faltings_height": 15.01267490470215,
  "conductor": "7113395464076270460963812563146382403574683726624988539070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "29",
    "31",
    "43",
    "47",
    "11437",
    "13296388428268243",
    "21958162070628266273420587"
  ],
  "discriminant": "3726853191461390037591948456052127785220962218671168858729305471990677154916352000000",
  "regulator": "8353416769798619.255105901832960113079918468444866285856163552026164561584058",
  "points": [
    [
      "295735275876774",
      "4795231050403005885213"
    ],
    [
      "306533351149574",
      "-5080448564154116577187"
    ],
    [
      "72688646518014",
      "128038100147956804053"
    ],
    [
      "7655270007331326/49",
      "-543209652564388042775541/343"
    ],
    [
      "72883353075654",
      "131542452070972911453"
    ],
    [
      "-91872736911726",
      "838743004990625914713"
    ],
    [
      "37989913930374",
      "276643499085382634013"
    ],
    [
      "608434543148574",
      "14793864909384927269613"
    ],
    [
      "400972313766342",
      "-7772796346231779874467"
    ],
    [
      "-5503615287908874/49",
      "185165769642304506668859/343"
    ],
    [
      "-12536900280906",
      "765974574513289118973"
    ],
    [
      "53214586810374",
      "-39408700266737325987"
    ],
    [
      "53117467067334",
      "-42653327973939129507"
    ],
    [
      "1063346529875574",
      "34508662841769887135613"
    ],
    [
      "634856793771766/9",
      "-2329238617080859920049/27"
    ],
    [
      "74170183990374",
      "154059655728921395613"
    ],
    [
      "-112651808054226",
      "-531528141919688532987"
    ],
    [
      "652815494995674",
      "16472145489466414346913"
    ],
    [
      "131185744306374",
      "1110665530563635042013"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 5/14 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -43445529415244318917275T^8 + 422168252009965455353400T^7 - 1000615470852214740048840T^6 - 287665459520844013324560T^5 + 730836999165531608469360T^4 - 1534018519968751162419840T^3 - 860145796269947075014080T^2 + 1257969101915425406539680T - 287979670569444598886832,\nA6 = 3481769198723618054364520888653750T^12 - 51546572699746324664281711293253800T^11 + 257425214170732002290334218843166696T^10 - 384910798826712681438480236614322160T^9 - 547380365950409455224187028746997760T^8 + 1186458230569584965410644869136438720T^7 + 1903926669733832318282196311637144960T^6 - 342699085864060966883864121127625952T^5 - 1605189770963765735095620014272121520T^4 + 273990330917492951575782706024802880T^3 + 722163883191450327543709222733194560T^2 - 391773240304041316040915337560972160T + 59143024921117996675555945526480256.\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": "2026-10-25 16:37:46",
  "updated_at": "2026-10-25 16:37:46"
}