{
  "id": 6161,
  "curve_key": "772096323068492099433229201:-21879954507382037511401182131466847006905",
  "ainvs": [
    "1",
    "0",
    "0",
    "-16085340063926918738192275",
    "25324021420579721489486781705228816161"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 185.7727790502642,
  "faltings_height": 13.375664807094838,
  "conductor": "89594375732498958534425926758310931225832431484559479620143267614",
  "bad_primes": [
    "2",
    "3",
    "17",
    "29",
    "11481007",
    "102887515043",
    "25641292813895526753998749543866217207971133"
  ],
  "discriminant": "-10683170563136582386614939888565004590003856869944336740598952042513077854208",
  "regulator": "7879094214942329310.86009196478772086483289114418020886019969982618091730416355",
  "points": [
    [
      "1781680838126",
      "-1523425666765770247"
    ],
    [
      "3044557434116",
      "2138289200935436153"
    ],
    [
      "2674053708398",
      "-1196641762778389351"
    ],
    [
      "9651806779454",
      "27734601753470850521"
    ],
    [
      "2184907067378",
      "-780641132163238111"
    ],
    [
      "-11508355634",
      "5050656964045516153"
    ],
    [
      "95205664708430",
      "928142906974005236729"
    ],
    [
      "235183147226",
      "-4642631780960475247"
    ],
    [
      "5847455040110",
      "11454523368272138489"
    ],
    [
      "4803457733486",
      "7673975773892734361"
    ],
    [
      "3899419291262",
      "4678998186472385369"
    ],
    [
      "1935661519070",
      "1200314066650966409"
    ],
    [
      "1821036145634",
      "-1439065189383111715"
    ],
    [
      "3108812504030",
      "2315922130422561929"
    ],
    [
      "2213025350462",
      "-751670010535831591"
    ],
    [
      "6771437919566",
      "15062852479946700281"
    ],
    [
      "11251270649114",
      "35618165803522725845"
    ],
    [
      "-3139105409938",
      "6699621618364776089"
    ],
    [
      "1457132170664",
      "2231453447931204695"
    ],
    [
      "2691799818062",
      "-1236816651763239751"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 25/24 of a rank-17 fibration of X1008 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -3261288267173019191472T^8 + 16336709243720609162688T^7 - 18268306752455049094272T^6 - 19274483100900643686432T^5 + 47527616284455427617672T^4 - 42492106937679957084528T^3 - 37117805963754630710128T^2 + 57264934594581910892472T - 17428523548140354643227,\nA6 = 73778746260046465803130020065664T^12 - 557691636286597619819213618736384T^11 + 1241644089075433039709482561447680T^10 + 319292057952411507722665432506240T^9 - 3684776099503733525147843819041632T^8 - 105975540379555346975431938448896T^7 + 6959425978364243633608708638354240T^6 + 2168365187018207896801103646494784T^5 - 9811177379114913645781233251073240T^4 + 1286921179016092176554695571280336T^3 + 6464160388118625330104562158316256T^2 - 4394066368078192631786533039340328T + 883707771835909746830128944197430.\nIt is a 2-neighbour of the fibration given in curve#3589: 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": "2026-10-29 21:06:20",
  "updated_at": "2026-10-29 21:06:20"
}