{
  "id": 5797,
  "curve_key": "58686612460260379538550395376:-14220017893673988538032551279407070472788376",
  "ainvs": [
    "0",
    "0",
    "1",
    "-1222637759588757907053133237",
    "16458354043604153400500638054869294528690"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 198.72644917693958,
  "faltings_height": 14.280082575105034,
  "conductor": "3056054011786488346217011870527784738133210011523115704645",
  "bad_primes": [
    "5",
    "11",
    "13",
    "17",
    "23",
    "29",
    "47",
    "61",
    "139",
    "7237",
    "23893129313",
    "792035580053",
    "6906554409991922453"
  ],
  "discriminant": "-49341592874226230827565586188636395022008596369205068806622754896030849140796875",
  "regulator": "14834441324571168.19843791142069474527315984199607586373163684674514159460090",
  "points": [
    [
      "36288675696893",
      "140988808393060553997"
    ],
    [
      "-253880328801668/9",
      "4558171244812211681999/27"
    ],
    [
      "20302120068663",
      "2064872629071698957"
    ],
    [
      "19837345718623",
      "-3296067658998480163"
    ],
    [
      "19978181802198",
      "-2474129864137672813"
    ],
    [
      "-5646156271565",
      "-152254929728579160555"
    ],
    [
      "20545389344905",
      "3355839241879593930"
    ],
    [
      "20001081262873",
      "2361026177121338837"
    ],
    [
      "19713165148023",
      "-4123712534961890163"
    ],
    [
      "-40088140039302",
      "-32366999458911540313"
    ],
    [
      "322012162595593/16",
      "123153854665845480443/64"
    ],
    [
      "7137493583323",
      "89974418753329366437"
    ],
    [
      "20021823109648",
      "-2265703157830274338"
    ],
    [
      "18714412133608",
      "-11477853155314875258"
    ],
    [
      "-2498630459277",
      "139634074119459199637"
    ],
    [
      "6588205026472177/324",
      "-12734419815201750836941/5832"
    ],
    [
      "197473558818682/9",
      "-377162804265269216851/27"
    ],
    [
      "-40643301324863/4",
      "-1334642065800522452549/8"
    ],
    [
      "20135987130879",
      "-1905904662059311843"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -23/50 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -9879263860426790634432T^8 + 86542933653687887807616T^7 - 135085452380206943680656T^6 - 670355493830703722869488T^5 - 1051946747940271972123080T^4 - 3373640011473668508665088T^3 - 849884467368517694646336T^2 + 3646401529809912988876056T - 1342215706985392840165467,\nA6 = 376157002259901169222608370611456T^12 - 5012568105195271642968657466363392T^11 + 20939308987938975132973897671040896T^10 + 13327362718284003523861442478906240T^9 - 278883358041208378819482351125270640T^8 + 367979789534049131266298576914822080T^7 + 2889329182749276846125866347500564400T^6 + 1554211227618089538131391252658550640T^5 - 3013942383637349393404424222146644840T^4 + 631952356094086111413853506833246400T^3 + 2160468957381686900407596405190211280T^2 - 2226612923028643159215506958258590280T + 628996598302785742517854074617969910.\nIt is a 2-neighbour of another fibration built here (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": "2026-10-25 10:35:23",
  "updated_at": "2026-10-25 10:35:23"
}