{
  "id": 6164,
  "curve_key": "73872478454937518242388669715647001:-20320012711476170642422073504060163742820741301045501",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-1539009967811198296716430619075979",
    "23518533230875197887555817767684022955520549793353"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 240.88689198194237,
  "faltings_height": 17.94652144058767,
  "conductor": "791611698628038475107292196100229160812371724694342056749341780312711879429177670289845030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "53",
    "2521",
    "5984505821978086381294720657513510569250479881284929532648767545775099451848064369"
  ],
  "discriminant": "-5654069735702168962636238480686719651232697780730188385563467742370712953695463640019724467568112500",
  "regulator": "19718019324819264419452656.509594788402045997427597496227388151776183397670433539645655",
  "points": [
    [
      "21519195314131717",
      "604396397048041324040554"
    ],
    [
      "9176290627447627",
      "3188857738460679684988579"
    ],
    [
      "20665421767030198",
      "734582231515977027187651"
    ],
    [
      "15997193115544492",
      "-1729895455689126275448971"
    ],
    [
      "324265802319990397/16",
      "51687019854569587594163281/64"
    ],
    [
      "-128239642206491657/4",
      "50537378065454860445290607/8"
    ],
    [
      "11376272254192867",
      "-2735443133052834248953646"
    ],
    [
      "33514771905687142",
      "-3095819043416387616155621"
    ],
    [
      "22667841124045132",
      "-529093335750519589724171"
    ],
    [
      "3038739654657670153/289",
      "-14322751787516149063468568998/4913"
    ],
    [
      "42056346211639423",
      "5760206708697235907738866"
    ],
    [
      "-5002360340709068",
      "-5576023540192611358710761"
    ],
    [
      "-9389728989145952",
      "6094387209815325066144541"
    ],
    [
      "108146025493057363/4",
      "10344553208997844573072157/8"
    ],
    [
      "23555356011709702",
      "580006719084671753340079"
    ],
    [
      "23087909290961992",
      "541347063154523682296029"
    ],
    [
      "25658510054116262",
      "960387963489804170852859"
    ],
    [
      "55100982134020963/4",
      "-17766931455724630331193583/8"
    ],
    [
      "-308772605681762879/64",
      "-2842928049368724354342572653/512"
    ],
    [
      "24017060638495852",
      "-639952553763367044701921"
    ],
    [
      "-1091142339830108",
      "-5019612839431638278943371"
    ],
    [
      "-4255352266884506",
      "-5476358894967829388682725"
    ],
    [
      "-20041433045029931",
      "-6805341695536753865230550"
    ],
    [
      "32859053575746052",
      "-2902863120410124218373131"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 50/43 of a rank-17 fibration of X1092 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -906180833179571257456587T^8 - 1930046192084997346024728T^7 + 6011648406192813483229776T^6 + 8355472943604505878941856T^5 - 9649478959250650200991080T^4 + 7450754699414011152778704T^3 - 27984481563110444272430064T^2 - 17758766835719522469182592T - 3317283523979050195432512,\nA6 = 332150243825525078123196022294739334T^12 + 1126061667323176712064227845083588744T^11 - 2713185092886283310031062058684874464T^10 - 12015892423153220327930309833774827360T^9 + 7554319779210673373159460328484862840T^8 + 58673243715970603365442249112691953136T^7 - 9754551868147305475783193074338006384T^6 - 149812543158867507723474722158888312896T^5 + 23811683678756345915421047541045697680T^4 + 99714459519208696131901088663865684480T^3 + 64761255203716406202557626472759415936T^2 + 18947601952381150031159658003937314816T + 2277468715827369848274981635668809984.\nIt is a 2-neighbour of the fibration given in curve#728: 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": "2026-10-30 00:51:53",
  "updated_at": "2026-10-30 00:51:53"
}