curve #4088

y² + xy = x³ − x² − 17503967055046696205704545730902468530138328804x + 894626890628394372235486258020137581791958557048134993037737763309860

a-invariants: [1, -1, 0, -17503967055046696205704545730902468530138328804, 894626890628394372235486258020137581791958557048134993037737763309860]
c-invariants: [840190418642241417873818195083318489446639782601, -772957633502932737611456346072514980581871761107710759051402917620697349]
rank (lower bound): ≥ 29
torsion subgroup: trivial
conductor (N): 524916760800922554989679230760923419479510811217039491939502038238822921046652182045653134297852238608502059531483464570
discriminant (Δ): -2521026405277514404665494760060234186080604307430298682607095926552922694297358286798304391052929519088962388772335838536218584272988062500 ★ record for rank ≥ 29
Faltings height: 25.4111 ★ record for rank ≥ 29
naive height: 331.0572 ★ record for rank ≥ 29
primes of bad reduction: 2, 3, 5, 7, 23, 41, 233, 367, 5503, 216899, 67036169, 136032497, 1594719463, 595282339499346020925110209861716919706725722023068681145445205610081422741
regulator: 3497403594236465106581511831243291.51655291926212586373855633809002157979854369384653636714383139
submitted by: Matej Jurasić
submitted at: 2026-10-09 11:07:27 UTC
last updated: 2026-10-09 11:07:27 UTC

Witness: 29 independent points log in to add more points →

(138548282766496961424991, -33600646178082231742676039599563938)
(63487670178631601358121, 6264148514499972284965692790362127)
(50518438661987200715434, -11801802859065707827471602461898848)
(1778239474135770512381314/9, -1937522010087987503031825929783874896/27)
(8820131311009084609671871, 26191718553593248821725983037427213502)
(-58918258817111406544544, 41489801071810734676201013927888362)
(342421318758320239492039/4, -38808824533331630832703151894545429/8)
(71560098682394269728631, -2913700269851825637647348517769418)
(-1025755448488675198130786/9, -1013532189644698242104052887894635696/27)
(12356246442932587957328239/169, 5238073162221361492461175578670831054/2197)
(90420290644213723781341, 7153595803573755607142825657952172)
(76756334959228052823136, 1816359758192635162967291719823722)
(27069476172926232717347456/361, -13218555271607234294401680994070513982/6859)
(-356917323751240179260441/4, -334287207228499531379076880788152209/8)
(96559522255140057414421, -10234656978411499803556380368760473)
(41156991728813398263421, -15618322828918094131798496615238473)
(-33085940616518288622314, 37914952266148833702195494367604192)
(13520816475680597311696, 25698847025638894368773747152187602)
(52274894785020754341653824/729, -56288924736602554695188125692596539954/19683)
(79634098606320960748180129/1024, 63101084978771220968689446842830874111/32768)
(228724009038068331848659/4, -71864471612886833317110464349418759/8)
(-16628380429586790105118544/121, -35334633262304461668075072757161793498/1331)
(-309889947163195833977341/4, -338061670089547611017356916363523259/8)
(3989896946365820799504034099/27889, -169121119123914867081932610427158952633714/4657463)
(401627853498930298132325506/6561, 3851193157248962470052972531222120787632/531441)
(4362940235233382395218790714/29929, -196536355032161662468540910752749196631776/5177717)
(1046761362889709215413077623744/68873401, -14370515758960683230221687094756089461970605074/571580354899)
(36593229307083115316875490664016/290395681, -129976105768639281673770294355461009183340994318/4948632799921)
(266616335052933998255074283599696/3226353601, -647127437117605442177840733256470639222602676898/183260110890401)

Commentary

Specialization at T = 1607/3549 of a rank-16 fibration of X1152 (two neighbour steps from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-09 11:07:27 UTC · history