{
  "id": 4170,
  "curve_key": "2477571950490785996642899399063735422867144496:-119565533346484101549092808801963638657039409445657661515954684594456",
  "ainvs": [
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  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 313.57082463930846,
  "faltings_height": 24.046589465848154,
  "conductor": "1598740076010203977106890461848627662726267706800893427358467211796174691199865947728895749564939904268799490595",
  "bad_primes": [
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    "29",
    "71",
    "463",
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    "520609",
    "1480708481663784570649",
    "169564185095878422973915902109",
    "1610685729850385606820172851348616368497"
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  "discriminant": "527962185248660500083241120869783059790627612102857686242563329967356891354889462319991412244019387187824473441903646389181203703125",
  "regulator": "4924808336656359263427708349848.0312849730893512297283929372591533195834336529714283394476791",
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    [
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      "-7388984982707763626948425062822012971/389017"
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    [
      "23591440283962171999324/9",
      "-3921716728790249625349836207715601/27"
    ],
    [
      "4792698034793369160311",
      "33072546298063520978577686783587"
    ],
    [
      "-8147295863158843568734",
      "134583879410452676910137436049477"
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    [
      "2813394955351542688301726/361",
      "-3139156257981068737178797173088593002/6859"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1163/397 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -8601190111439927121627T^8 + 70553802194275661608968T^7 - 40117514965744884873804T^6 - 394125757357369375667736T^5 - 727539205447352323463130T^4 - 3371639403550126915091304T^3 - 358500560703347306973924T^2 + 5575527756032095197563112T - 2574982297007819942866587,\nA6 = 311073935845060124132541860022390T^12 - 4299424530738788428378210804267800T^11 + 17883941445167312163435648485037300T^10 + 19652059401694206221665695004579800T^9 - 317465301013995782557083261357635310T^8 + 112305603376549774936723074091082640T^7 + 2598376408341179206723494257772920880T^6 + 911887687830002593185098844364676160T^5 - 4509956533653094383564183143089914510T^4 + 1581320920924061257174062701329500840T^3 + 3668404075692271898587012925610059196T^2 - 4676936909330964399995425467736251576T + 1568898839279682527117596188509969334.\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": "2026-10-11 22:13:07",
  "updated_at": "2026-10-11 22:13:07"
}