{
  "id": 4609,
  "curve_key": "45482890830568234422527784967547854592424513121:-9498876440222306483910392313162776633377565158108681028941786984209169",
  "ainvs": [
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  "rank_lower_bound": 27,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 322.3009962428153,
  "faltings_height": 24.75619201450327,
  "conductor": "123002866817579179599597934355591467598164984173082841396259480229356238688609053812425123766047888102610",
  "bad_primes": [
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    "31",
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    "137",
    "617",
    "6884381724913004470688326918874802467058900576346123822298751942151953125883446533663"
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  "discriminant": "2234664670784224944273556889649578016609425270762988365476466306176039961087386083196666358984895879922503394600649747919679219123200000",
  "regulator": "28307660299460390964986699967.792453733483416090956139307209414511254917392840727289978325910",
  "points": [
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      "239449964324538869706429826455134104202/205379"
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    [
      "22105043856129904747924",
      "-921663011140400907178403511224162"
    ],
    [
      "-34284093889001814615926",
      "-1784046189586091372958050576237612"
    ],
    [
      "4679517916771780061082776596/299209",
      "190385440621246738596803071160736268234/163667323"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 5411/3949 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -58701756188828782740672T^8 - 421589935203760423753344T^7 - 677464368389618755113936T^6 + 669015607734413855170992T^5 + 1311645217705022688331320T^4 + 1050713078894545198928832T^3 - 1636359720229735222434336T^2 - 2517746756775352549692984T - 810344655390742277047947,\nA6 = 5480627817022307258018449212308736T^12 + 59387395680501866438327388746270208T^11 + 202192728222021747784840349845289856T^10 + 81426836279267976104124948661760640T^9 - 731444121000417496333010776856855280T^8 - 504969396495943282941884145271012800T^7 + 1906585932510725663650827845073118320T^6 + 512612498829370479665585111044169040T^5 - 2456755728368285626110680543972723880T^4 - 642737286070578650255592249597744000T^3 + 1935352237260464424985879727209027440T^2 + 1451023268234470568001166626460852200T + 303174450039421684871841546202620870.\nIt is a 2-neighbour of another fibration built here: 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": "2026-10-19 02:21:46",
  "updated_at": "2026-10-19 02:21:46"
}