{
  "id": 4226,
  "curve_key": "20034672811804997682322026118520016:-2812498651922327416615254829578709981935204519935640",
  "ainvs": [
    "0",
    "0",
    "1",
    "-417389016912604118381708877469167",
    "3255206773058249324786174571271655071684264490666"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 236.9483174457824,
  "faltings_height": 17.60237378425998,
  "conductor": "80151163480449143652638260373196573000359294842516282152443251449303489021117",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "23",
    "29",
    "43",
    "67",
    "79",
    "265523065253",
    "220716503477760798348504972643581656125444870309526437"
  ],
  "discriminant": "76117407996287559815040621810294938793138761104990662832222746415859210066543089838851172111389557",
  "regulator": "8435367235421159453016.17527464202440828415537502339993852026987618707270564646249323",
  "points": [
    [
      "4761433121225049",
      "1172938405070423032553011"
    ],
    [
      "14559052061632347",
      "-514239565302132303549416"
    ],
    [
      "-8679564207241659",
      "2494812219150031981015315"
    ],
    [
      "12729485296188237",
      "-68866674523597078867085"
    ],
    [
      "9214828759715694",
      "-437604669733570053776177"
    ],
    [
      "8674139363463843",
      "-536063927632546069913657"
    ],
    [
      "633166680814137066/49",
      "47746537282684040027933749/343"
    ],
    [
      "133278390080710143",
      "48115148773166224839621031"
    ],
    [
      "1174810852313367",
      "1663272400248361775732359"
    ],
    [
      "10870222716010927",
      "-50394949342484263632616"
    ],
    [
      "5720447451626484",
      "-1027009253153685793556219"
    ],
    [
      "3659499446439105",
      "-1332958994051177626580948"
    ],
    [
      "1498718202688783233/16",
      "1794309941478750410786973727/64"
    ],
    [
      "382196718583963552",
      "-235950971046584771085618010"
    ],
    [
      "12734287525269579",
      "-71228917130274794894504"
    ],
    [
      "-14262521085450369",
      "-2511364451779602322258856"
    ],
    [
      "-6860131556901972456/1369",
      "115738884549605188247327477725/50653"
    ],
    [
      "10701044018773377",
      "-118786170244522889724116"
    ],
    [
      "-20877239955770487/4",
      "18402624487508550668600945/8"
    ],
    [
      "14829318989190744",
      "-571583925976820286041474"
    ],
    [
      "13662222786173230",
      "320757572536491038976527"
    ],
    [
      "37202379203097223",
      "6262273407609015047334968"
    ],
    [
      "10206135094154268",
      "241665299981935808572093"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -485/27 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -13129724922135998400T^8 - 393315956007325349760T^7 + 5388075614914218900720T^6 + 133624136603638823580000T^5 - 2980942426742659655805540T^4 + 33575588298751816593482040T^3 - 178476287434090182905197255T^2 - 27064681539446356514316710T - 38737534397522382035015527,\nA6 = 17001575848734905085648825600T^12 + 808662010058021550277497323520T^11 + 2204274099561464081452163602176T^10 - 450617120852864904310146381112320T^9 - 6041711991147376183046964974244960T^8 + 125500678000542015284784371883062400T^7 + 2667323428245326791597400104572570240T^6 - 56072697432225196572060046394633385120T^5 + 291328099318551627699751437189468287265T^4 - 366248679959978292773278702918063389000T^3 + 804324836109783714230677491953667748735T^2 + 249729199613745513617677147674877497230T + 91023269067533367175532101155650107690.\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": "2026-10-14 14:43:19",
  "updated_at": "2026-10-14 14:43:19"
}