curve #3822

y² + xy = x³ − 350641040539906639296716341465077279615362155x + 2428476189504593306349617350890720820305100352810443675940491049777

a-invariants: [1, 0, 0, -350641040539906639296716341465077279615362155, 2428476189504593306349617350890720820305100352810443675940491049777]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 577113588286798462082842398737793192182866872243232463868455218334881358894015008354567258327723110
discriminant (Δ): 211386372561620544096295520049179776142390894128988741012736789596030198827769747879297821844863774229992630686406931502556643328000000
Faltings height: 24.5374
naive height: 319.3186
primes of bad reduction: 2, 3, 5, 7, 11, 19, 31, 37, 53, 109, 294026806471, 2014504829122887844121147, 304566413251820761938610305141974327766679193657503
regulator: 1488014464865331401089962805.35882686744660532607737961489440036625373438994404536146376108
submitted by: 7fff-zip
submitted at: 2026-10-03 05:21:27 UTC
last updated: 2026-10-03 05:21:27 UTC

Witness: 26 independent points log in to add more points →

(-11623563781454039138626, -2221203981053085892905520730055007)
(18251340884322805312382, 1452080420929297574937300648385313)
(9015792651230256907454, 3691230741944520210730057577633)
(-810726949712700058964194/49, 659830939476891142802154049003450679/343)
(7685395724194956925094, -433129653849141668609713026252847)
(2575996959729170105534, 1241901619922739612128197893829793)
(8997027827185424197094, 45022115744395089986667319358153)
(-17245257487378992198106, 1829385282601799429074856837689553)
(8368351855740883923518, -283228735789810091037638734070239)
(-9093332441731410198466, -2205687182482527532735373967754207)
(13371446271741314767724, -361460627624769361686271257470767)
(1010259911269904442783734, 1015256027341737919381423298134811993)
(-10813494943120018668946, 2226138193110672430928831736970433)
(17489699490508907509694, -1282882199398257319636862179991647)
(-1983673254816050463106, 1765284047848004466491871283723553)
(7954740045493542371014, -377593725949252718012575094264687)
(12693081177086527493444, -150990100974370039425203534951647)
(8677849683719301091874, -197868818123039683756048303285867)
(13354095427794339098174, 356991613595486193361245301414433)
(14361974403313477224382, 595793577683015875701097393041313)
(12931315717830525289694, -237880052277329135441049830378047)
(20338232834046818517694, -1926094298848106881971982166814047)
(29427500970353825288894, 4194466541958420047100663061627553)
(15364330291778732665324, -817346854754894337649023808911407)
(109207639218935424461838026/529, 1136700326216294926854298811229428124751/12167)
(1083891602183187349765526/169, -1462998572126114236367759360684236099/2197)

Commentary

X1092; T=977/498; 2-neighbor step: yes (trace v=[-1,-1,0,1,0,0,0,0,0,1,0,0,-1,1,0,0,0] in source section basis; height 12).

last edited by 7fff-zip at 2026-10-03 05:21:27 UTC · history