{
  "id": 4203,
  "curve_key": "48367414687152819896291513075110713310760256:-275268857560379529135562918376366361211217029705303372518008244096",
  "ainvs": [
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    "318598214768957788351345970343016621772241932529286310784731764"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 301.762200727417,
  "faltings_height": 23.150686848159616,
  "conductor": "19834100158182773487723967518986340699072465094418945166043502766109655929803468704702942705080",
  "bad_primes": [
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    "5",
    "7",
    "13",
    "19",
    "29",
    "31",
    "37",
    "43",
    "47",
    "61",
    "89",
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    "167",
    "2719",
    "137293394641841021422073434861271",
    "124799616451944482251749586040176426183"
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  "discriminant": "21630853614093693837362284794469412620847618653623339834332889415027341016292666403945320171786699383194129255593301231700000000",
  "regulator": "656374557138509808513580005.464499161071905166455463291053535349698695168683795729192627003",
  "points": [
    [
      "-295823494465667405407",
      "24306338937594110714389707632725"
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    [
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      "-65194317084895185097767162916610"
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      "-124272549238275770502",
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      "-128293320497272993680534492/143641",
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      "4029675727919062917918",
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      "-913959677422776882",
      "17875099148320347424519491813350"
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      "236017143523517329118",
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      "-120855699389748890643658747252178"
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    [
      "-1077578356549011445207",
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    [
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    [
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      "12203721588679435838613965264750"
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    [
      "1250878655246798047118",
      "31865205716383859039025026234650"
    ],
    [
      "844767590291839652268",
      "8379606014036269554397140562550"
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    [
      "-20884576293745025824026/25",
      "3003620785973389088830409005901618/125"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 388/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2350796244229826784432T^8 + 40408811499609701188800T^7 - 807647185297995630241792T^6 + 1124780763822387162339456T^5 - 1304766910580579021664360T^4 + 1443539650170624433343496T^3 + 1704268062115609657765788T^2 - 1468913167837302046081776T - 1000351384601036369237532,\nA6 = 39869593619137462773895754588544T^12 - 1348966735043080317092632272134400T^11 + 31027342372605406058463256507914496T^10 - 139468061144328757444897112746057728T^9 + 1081825061951776499965823580935603424T^8 - 1898481303093606040657233497704979232T^7 - 570283484013752985306584054565000912T^6 + 2509799809819326794944663142993968224T^5 + 574280708473637397501657996019459428T^4 - 2029433790678638479785535621658530032T^3 - 641250037642162230715032671759921448T^2 + 863840080098002956108405878211611888T + 384816973441734885044295380206073844.\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": "2026-10-13 02:28:26",
  "updated_at": "2026-10-13 02:28:26"
}