{
  "id": 4596,
  "curve_key": "1496680669364923626890778755705105973121:-57660427017145655141050718929587858295818943617580321462081",
  "ainvs": [
    "1",
    "0",
    "0",
    "-31180847278435908893557890743856374440",
    "66736605343918582336580668895301473212364323476878081600"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 270.61220518719955,
  "faltings_height": 20.379461966469098,
  "conductor": "123226310933262615847910201689318930893780182413475658859257710637903282103668438810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "29",
    "31",
    "103",
    "191",
    "5944579",
    "482763421193147",
    "443725827229977059",
    "12448426897419592085712173594953"
  ],
  "discriminant": "16156955233106339020067315994684713363069757263676035115482748359738116426961633595817413603509684022865920000000",
  "regulator": "995779081930479609016831.16429224775633921318579735249115984015816824351633912867575679",
  "points": [
    [
      "3581955085836954320",
      "1003063007300751780012869720"
    ],
    [
      "1354052840227682480",
      "-5196026465168235499237183240"
    ],
    [
      "3023548846909310420",
      "317196103109692472714875460"
    ],
    [
      "2901387554057128919120/1369",
      "161557478196782653684480535644280/50653"
    ],
    [
      "3670008105755379680",
      "1316751157377517845252124760"
    ],
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      "9648665918044266320",
      "25770962419851708948656015960"
    ],
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      "3019731385692404240",
      "-339236244626293408095331240"
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      "4484472139547938986490185260"
    ],
    [
      "5228502060843001280",
      "-6829367788294326862944931240"
    ],
    [
      "1189500813061547480",
      "5597320907471521973602591760"
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    [
      "4285614827573920880",
      "-3437909957040905075037847240"
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    [
      "2523333785192695682",
      "2030646354852065017200367946"
    ],
    [
      "179444965314695836880",
      "-2402641942294284442160652729640"
    ],
    [
      "680263062223363190",
      "-6770540876272920750564911740"
    ],
    [
      "32608347059082244580",
      "-183637077677278754936078801740"
    ],
    [
      "-2786633639347924054",
      "11488563084883270982089360802"
    ],
    [
      "13921532190997297295/4",
      "-4888668890258850304795007795/8"
    ],
    [
      "1154491271186673680",
      "5681316143902100716225641560"
    ],
    [
      "4507235854782861680",
      "4214553104836072239231304760"
    ],
    [
      "-56129581766264455280/9",
      "-116518917552669459151109239480/27"
    ],
    [
      "3423650262496814480",
      "-337933311967610065077091240"
    ],
    [
      "2978127463004345600",
      "538334887088042838477071960"
    ],
    [
      "969306742077490520",
      "6117476390343192307083109520"
    ],
    [
      "3027928025162027600",
      "290417379293591183930831960"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -89/129 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -131683424850520935576768T^8 - 403203691800547711440768T^7 + 228773565844968202575408T^6 + 1001632750223305381512624T^5 - 240565012803414935795880T^4 + 1113998583596965801461504T^3 - 955469793798674292115872T^2 - 990503756503270017161688T - 226533255431841379251243,\nA6 = 19076424418751512058704915856577792T^12 + 97086137010965231517170399109938688T^11 + 56104518594343130212702088417622912T^10 - 478767125533383624912178730778518400T^9 - 714366843201118889959457857278267504T^8 + 1042906926398973532541608382597231424T^7 + 1920199847343299876864028118527850608T^6 - 1651848617855242258127597768465390256T^5 - 1294346250171073842969926939033547144T^4 + 242314299085392499926732997139536320T^3 + 623077991032626826626842144461126512T^2 + 269831263748284750614515352678364488T + 41099644923330823113323890449407142.\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": "2026-10-18 19:42:30",
  "updated_at": "2026-10-18 19:42:30"
}