{
  "id": 4554,
  "curve_key": "1274841985128983556185148740785784961:-1458024755484001930514392475641176861800910334130767041",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-26559208023520490753857265433037187",
    "1687528652180557796587015519353707019252407022762499"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 249.4333552683815,
  "faltings_height": 18.661813420765963,
  "conductor": "663374512441231775244000065310658129112072096871191143483321476920768010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "41",
    "59",
    "67",
    "109",
    "266647",
    "224680467559",
    "1636226654825959639",
    "81847462680561325593697"
  ],
  "discriminant": "-31212289280637684803783467392949391351864425222487670136101082813307760047293555078566390610521600000000",
  "regulator": "460489485447418278549.8779311162795245517949740057298875629204226729167902377395099",
  "points": [
    [
      "-59544629793672683",
      "-55297989346375745204580754"
    ],
    [
      "288543243977568907",
      "134340433961982394661302946"
    ],
    [
      "935533600459095307",
      "891987180800378437258113746"
    ],
    [
      "127398125419457107",
      "19278041462893566547660946"
    ],
    [
      "83916418721613259",
      "7050641213189512290190178"
    ],
    [
      "64278479073302707",
      "-15681964743241711422796654"
    ],
    [
      "145295050884374347",
      "-29931261324182508182331694"
    ],
    [
      "97700431338147547",
      "5026903280304618528427346"
    ],
    [
      "473705470582287067",
      "-308875885945416546701678254"
    ],
    [
      "-86866372166027813",
      "-57785442153359578401161134"
    ],
    [
      "308630058474450907",
      "-151288953425878586583143854"
    ],
    [
      "74306595474407707",
      "-11148361930463729350876654"
    ],
    [
      "2444454845375737",
      "40281763539300446874626696"
    ],
    [
      "94972202069334427",
      "-4665273051463630800830254"
    ],
    [
      "108759881520267227",
      "-9243464299667470908062254"
    ],
    [
      "-33956189427636443",
      "-50499761272050876685462804"
    ],
    [
      "229765186325624107",
      "87834619334247100409746946"
    ],
    [
      "1479763827038833237/16",
      "-302011109310757259725653931/64"
    ],
    [
      "17011621512904095523/169",
      "12812784717019352505936699962/2197"
    ],
    [
      "92082088811689387",
      "-4761886195072564354974334"
    ],
    [
      "521101679771726107",
      "359654080871620856773876946"
    ],
    [
      "42783635761643227",
      "-25090676105646812860940974"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -93/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -149283522995912209072T^8 + 7771051548175580374080T^7 - 96425969122530373515360T^6 - 650745155405088927481120T^5 - 2415911230346916965685840T^4 - 7601154786891989779697040T^3 - 2330949979661939283434680T^2 + 13731963511608379552174620T - 24775768582367122920991275,\nA6 = 728648747539615441339595057536T^12 - 56522770035420299634338505890560T^11 + 1220976136746860242842754846581120T^10 - 4534650284415406223365909009522560T^9 + 40082563358095594076415076965738240T^8 + 962506828193107880044950195752958528T^7 + 3523430440764385275475987785896930400T^6 + 2285241161704333099311601789013085360T^5 - 1404773498516823569998513341965901420T^4 + 18727747445156873508749884432613320280T^3 + 13182091133577376201427412811936218796T^2 - 39167275224385873529615083153972312500T + 47401684956970697155653713375708163750.\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": "2026-10-17 23:03:22",
  "updated_at": "2026-10-17 23:03:22"
}