{
  "id": 4647,
  "curve_key": "94632860725615593182909586965200:-953383505739034261874846051473686189395647480000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1971517931783658191310616395108",
    "1103453131642400108886205668726998949002460288"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 220.9526928537812,
  "faltings_height": 16.3336966113932,
  "conductor": "1125467240871469352139874526769622102961337464418348581287238549074200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "97",
    "107",
    "151",
    "711287",
    "9611713",
    "141111683",
    "511910705480893",
    "5408878389097816019"
  ],
  "discriminant": "-35571203038792136457626678262540443231442981046926775281806570199364022932784891985564000000",
  "regulator": "21308351768320244243.103536397222483084371204224971095029612252311842038731254004",
  "points": [
    [
      "1522078215642837/4",
      "-161661253012059037077225/8"
    ],
    [
      "1068873334337358",
      "-14742031776681146551650"
    ],
    [
      "1278754981101792",
      "-25950013285177781875152"
    ],
    [
      "2293139171853108",
      "92956609545880353134400"
    ],
    [
      "1179913546085328",
      "-20491542371101997172600"
    ],
    [
      "10633690849616658",
      "-1087450038440116562254050"
    ],
    [
      "790541506657908",
      "6240186974384123317200"
    ],
    [
      "2941836389475408",
      "144095116973955005212200"
    ],
    [
      "-1435616860099872",
      "31224945795389638026000"
    ],
    [
      "-1589930746073322",
      "-14794469490290478784950"
    ],
    [
      "1897250929792265178/5041",
      "7289063472016772998067820150/357911"
    ],
    [
      "3143488028421858",
      "161147263270980371696850"
    ],
    [
      "-283027120421742",
      "40481779493595789137250"
    ],
    [
      "6074355430978182",
      "461798730243255228151482"
    ],
    [
      "811538303991378",
      "-6161607800073305753250"
    ],
    [
      "10760843484311157/4",
      "988553405189821452510375/8"
    ],
    [
      "664545989456928",
      "-9314854192248984640800"
    ],
    [
      "491686012563534",
      "15904494942839939727774"
    ],
    [
      "-47392761845466",
      "34594542399245973341274"
    ],
    [
      "812806778065938",
      "6162364849362352634850"
    ],
    [
      "836603929221408",
      "6294259725931292068800"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -5/46 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -55167841848013120672432T^8 - 332957956141194498177568T^7 + 30491322260931582308864T^6 + 1529425586966988026755040T^5 - 1952037697734560475124240T^4 + 2598926506840431770721968T^3 - 1867830095998069273733704T^2 - 277424385594374102335720T - 14777266661889408077275,\nA6 = 4598281008482828350515082915932544T^12 + 42978899384640031706121578829901184T^11 + 92492192628018200121094722387755072T^10 - 190123782916092378560803318012553920T^9 - 804112508567836069639299650095483056T^8 + 453677299928650241856349297890606048T^7 + 3341413915638233675031424423024721088T^6 - 4626422467332761770277917962033627744T^5 + 1280672988092416347275859838092852864T^4 + 274908311165313855430793313344325200T^3 + 204841690501474358540727164780007400T^2 + 26424146202979804837762201204291000T + 968816204643834101037115185253750.\nIt is a 2-neighbour of the fibration given in curve#4191 (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": "2026-10-20 09:32:20",
  "updated_at": "2026-10-20 09:32:20"
}