{
  "id": 5973,
  "curve_key": "16906233195372243917631860800:-2191167864289876469663008248929562062080000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-352213191570255081617330433",
    "2536073917002054435490550943826454017263"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 194.99243967868927,
  "faltings_height": 14.067219875685502,
  "conductor": "14574758999340624880130810214478793247772364291268217656405600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "37",
    "41",
    "61",
    "42416743",
    "159382173259",
    "27491510819347",
    "1689478886988284087"
  ],
  "discriminant": "17902285514729447423945876678033270382912753678286046875972770042678170304000000",
  "regulator": "520178938270898051.940599381645831230685934234104915164492674337545908865914542",
  "points": [
    [
      "11892463438923",
      "-5417627121472589100"
    ],
    [
      "15746549444418",
      "-29905660971896637675"
    ],
    [
      "8583158206107",
      "12053996330596142868"
    ],
    [
      "10138877353683",
      "-2696675272309943100"
    ],
    [
      "10215237716883",
      "-2025720310105136700"
    ],
    [
      "10282165102133",
      "-1272886598704558200"
    ],
    [
      "11734873559883",
      "4344410483522534700"
    ],
    [
      "11424093584949",
      "1820694555619843464"
    ],
    [
      "7637238272907",
      "17076245670367890732"
    ],
    [
      "73832926319904843/5041",
      "-8156487795538491790830900/357911"
    ],
    [
      "33872682630843",
      "-171667652605862539500"
    ],
    [
      "194220843161643",
      "2694527098856845074900"
    ],
    [
      "13459989323573",
      "-15292221946255801800"
    ],
    [
      "-7365319671357",
      "68779962859738392900"
    ],
    [
      "-21638244178077",
      "-5101814798711112900"
    ],
    [
      "10318219958883",
      "629971506856853700"
    ],
    [
      "3877535580843",
      "35052169351836499500"
    ],
    [
      "28488988871459307/2809",
      "-397637876795530885974900/148877"
    ],
    [
      "11849124610323",
      "5127748015207695300"
    ],
    [
      "11540230238043",
      "-2888744146926590700"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 4/19 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -62238598979262328847367T^8 + 114310404580625317891332T^7 + 345964098754055988215811T^6 - 432486848349735134109966T^5 + 175844415801606548060475T^4 - 539957014758046237778784T^3 - 3466666840492299593283363T^2 + 1375801562449141429517514T - 457847843272340951907252,\nA6 = 6231113960947468288851293055208170T^12 - 17986527908278999930497783451836564T^11 - 63510145446922339309436221943522517T^10 + 196072827486310127387111443914446460T^9 + 329896017984738220842162864843822384T^8 - 977730912392624912334102291243654336T^7 - 1090216443601797579432503967842970390T^6 + 2401580225827262855577615397568975952T^5 + 1437988402318580839377591372944875134T^4 - 1577869275593930979134666639990964780T^3 + 1723891172774355272317470092631767475T^2 - 538001952495578595025088868536038092T + 119515751079584041083046899484291104.\nIt is a 2-neighbour of the fibration given in curve#4187 (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": "2026-10-27 12:00:51",
  "updated_at": "2026-10-27 12:00:51"
}