{
  "id": 4232,
  "curve_key": "289960247030320456955186626528077861256254016:-4851570868422001952614731003389314592449302602050100544347784024064",
  "ainvs": [
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  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 307.1349532203853,
  "faltings_height": 23.484363625413238,
  "conductor": "6434609419411114392518370233005172295466214234133422996628607416819300269168594580294781406755228672665120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "79",
    "191",
    "277",
    "9720779799103543067",
    "145928143603050514603893653574754050024972430623083940865898646919490123429"
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  "discriminant": "486823963672333392582867722630903457554234289416613310036927824287345560159549127784869155025080378381995437663536649330880000000",
  "regulator": "1194660859165830912894171500910.8895895679015664839914926802109206481527119302399102809765679",
  "points": [
    [
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      "-11098801066633942193052538036500"
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    [
      "-493982288267120708750",
      "-92080239239550754075615072297875"
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      "5458253070675884498875",
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    [
      "4598020887139317531749845/2209",
      "4711773124774495437361435257691984560/103823"
    ],
    [
      "6401103820755014754528625/2809",
      "9034852978019857016391095335443763500/148877"
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      "-2384912079909926545955/4",
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    [
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    [
      "2667192352016921798725",
      "-92072502204840295547843392223400"
    ],
    [
      "319441183260748427883325/169",
      "67722902780713893546800011770429600/2197"
    ],
    [
      "51313647951794919063931/25",
      "-5395901567208689939221012281755004/125"
    ],
    [
      "-257180489199835982859874175/94249",
      "1221072834130143777782825572068980903100/28934443"
    ],
    [
      "-1907599197648762576125",
      "-100980759484179275186143134004500"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 5934/4651 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -76081088435681081513047T^8 + 352756680332626657087252T^7 - 82339513624259414646469T^6 - 901545658338022693466490T^5 + 229450949582480650416915T^4 - 1247200030321945517143512T^3 - 1146369340545356004506811T^2 + 1687352936729813079668190T - 411496468647819081255900,\nA6 = 8112841022538000650593845586374970T^12 - 57168146144925559393934264903441092T^11 + 74672050992321347131912066302099019T^10 + 277662613390589143744390101854640120T^9 - 608279964343956992513678172184166364T^8 - 775627450421715998790683046858185472T^7 + 1913663946413950754123492444913586362T^6 + 1711261933991806885632762747792403176T^5 - 2007957630504188399500442532556750554T^4 - 505502209838775107774478816852469020T^3 + 1225508258092292403296873724948672675T^2 - 576830173318718574016743233507280000T + 96363113602603152516124313597692500.\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": "2026-10-14 23:42:05",
  "updated_at": "2026-10-14 23:42:05"
}